A symmetry perceiving adaptive neural network and facial image recognition

Forensic Science International 98 (1998) 67–89

A symmetry perceiving adaptive neural network and facial image recognition P. Sinha State Forensic Science Laboratory, 37 /1 /2 Belgachia Road, Calcutta 700 037, India Received 22 September 1997; accepted 15 May 1998

Abstract The paper deals with the forensic problem of comparing nearly front view and facial images for personal identification. The human recognition process for such problems, is primarily based on both holistic as well as feature-wise symmetry perception aided by subjective analysis for detecting ill-defined features. It has been attempted to approach the modelling of such a process by designing a robust symmetry perceiving adaptive neural network. The pair of images to be compared should be presented to the proposed neural network (NN) as source (input) and target images. The NN learns about the symmetry between the pair of images by analysing examples of associated feature pairs belonging to the source and the target images. In order to prepare a paired example of associated features for training purpose, when we select one particular feature on the source image as a unique pixel, we must associate it with the corresponding feature on the target image also. But, in practice, it is not always possible to fix the latter feature also as a unique pixel due to pictorial ambiguity. The robust or fault tolerant NN takes care of such a situation and allows fixing the associated target feature as a rectangular array of pixels, rather than fixing it as a unique pixel, which is pretty difficult to be done with certainty. From such a pair of sets of associated features, the NN searches out proper locations of the target features from the set of ambiguous target features by a fuzzy analysis during its learning. If any of target features, searched out by the NN, lies outside the prespecified zone, the training of the NN is unsuccessful. This amounts to non-existence of symmetry between the pair of images and confirms non-identity. In case of a successful training, the NN gets adapted with appropriate symmetry relation between the pair of images and when the source image is input to the trained NN, it responds by outputting a processed source image which is superimposable over the target image and identity may subsequently be established by examining detailed matching in machine-made superimposed / composite images which are also suitable for presentation before the court. The performance of the proposed NN has been tested with various cases including simulated ones and it is hoped to serve as a working tool of forensic anthropologists.  1998 Elsevier Science Ireland Ltd. All rights reserved. 0379-0738 / 98 / $ – see front matter  1998 Elsevier Science Ireland Ltd. All rights reserved. PII: S0379-0738( 98 )00137-6

68

P. Sinha / Forensic Science International 98 (1998) 67 – 89

Keywords: Personal identification; Face photograph; Face recognition; Image processing; Superimposition; Symmetry group; Neural network; Fuzzy system; Artificial intelligence

1. Introduction Cases of personal identification from face photographs are quite common in the field of forensic sciences. Such problems often turn out to be tough, especially for facial images of suspected to be the same person but with apparent dissimilarity which may either be caused artificially by the use of disguise, such as wigs, false beard / moustache etc. or be due to natural reasons like aging, baldness, growing or shaving beard / moustache, changing hair style etc. The importance as well as intricacy of the problem have recently been discussed elaborately by Iscan [1]. He has observed that one of the biggest problems with morphological or photoanthropometric analyses for comparing two face photographs is that the appearances of facial features are likely to be altered in the two photographs, since they are, in general, snapped at different times under different conditions of camera alignment / orientation as well as of lighting etc. As such, Iscan has emphasised on the need of developing of a standard procedure in this direction, since in the most of such cases, each expert ‘reinvents’ a method to fit the case at hand [1]. Although the problem of machine recognition of faces has received a wide attention of engineers for about three decades [2], forensic anthropologists have not enjoyed the fruits due to following reasons. The works on face recognition technology, as available in the engineering literature [2–8], are aimed at full automation level. The procedures involved in the total process include segmentation and extraction of a questioned face from a cluttered scene, detection of features from the face region, matching and identifying from a stored database of facial images of suspects. Such an ambitious solution to the problem may take a considerably long time to be perfected. At the same time, an automated decision may not be acceptable to a court of law, unless it is time-tested and fool-proof. Again, machine recognition of many facial features may be obscured in cases of artificial disguise or naturally changed facial appearances as noted above. The works done by engineers on face recognition are based on different methods such as statistical approach [3,4], feature matching [5], profile analyses [6], neural networks [7,8], etc. Some of these methods make holistic comparison while some are based on feature analyses and they have their own merits and demerits as discussed in detail by Chellappa et al. [2]. No doubt, many engineers have taken up the problem of facial image recognition for their study, but, at present they are more inclined towards development and improvement of general techniques of pattern recognition while dealing with this particular problem, rather than focusing their attention to the practical need of forensic anthropologists. Consequently, such works on face recognition technology, though having enriched the engineering literature, have not yet turned out to be of practical use in crime cases, where a forensic anthropologist is usually supplied with one questioned and one comparable face photograph for establishment of their

P. Sinha / Forensic Science International 98 (1998) 67 – 89

69

identity / non-identity. As is customary for forensic expert opinions, it is also required that the final results of examination should be suitable for a convincing presentation before the court of law and this point has been particularly stressed by Iscan [1]. A newly proposed symmetry based approach towards facial image recognition [9–11], motivated by the need of forensic investigators, allowed both feature as well as holistic comparison with the aid of superimposed / composite images which were also suitable for court presentation. This method has been revisited in the present paper for an upgrade by introducing a capability to analyze ambiguous facial features so as to make the method a robust or fault tolerant one. Such an enhanced performance has been implemented by recasting the earlier method [9–11] to a robust neural network, modelled on human recognition characteristics of symmetry analysis of facial features aided by subjective analysis for detecting ambiguous or ill-defined features. As an interactive feature selection process is involved in the method, the method itself appears greatly versatile now. This interactive nature of the method has an advantage that it extends a facility to the user to exercise his decision regarding selection of features depending on practical case situation in respect of image characteristics. So, even though a full automation has not been achieved in the proposed method, unlike what engineers aim at, it is hoped to be useful to forensic anthropologists who are in need of a working tool to deal with facial image recognition problems encountered in crime cases. The paper runs as follows. In Section 2 characteristics of human recognition of facial images have been analyzed, since, the neurocomputing paradigm is modelled on the same. Section 3 presents the proposed neural network in a qualitative way. Examples of simulated applications have been cited in Section 4 for testing the performance of the neural network. Finally, general aspects of the problem and also of the method have been discussed in Section 5. As studies on artificial neural networks are not quite common in the forensic literature, Appendix A provides a brief introduction to the basic concepts of neural networks, while the architecture and the learning algorithm of the proposed neural network have been elaborated in Appendix B:. Readers familiar with neural networks may skip Appendix A, while others will find it useful before going through the next sections. In fact, it has been attempted to make the paper more or less self contained for readers belonging to diverse disciplines of forensic sciences, since apart from nearly front view facial images, a large class of flat impressions or patterns occurring as clues in crime cases may also be identified from their photographic evidences by the proposed method.

2. Human recognition of facial images The fundamental principle of designing artificial neural networks has always been modelling human brain mechanism. As such, it would be worthwhile to analyze the characteristics of human perception and recognition of facial images for developing a neurocomputing paradigm to deal with the present problem. The psychophysical and neurophysiological issues relevant to face recognition have been discussed in great detail by Cheilappa et al. [2]. The face is the most individually recognisable part of human

70

P. Sinha / Forensic Science International 98 (1998) 67 – 89

body and we all are attracted by human faces from infancy. Human perception of human face is based on both feature as well as holistic analyses. When we have an experience of viewing someone personally, we can make a 3D perception of his or her face from the different retinal images formed in the two eyes, i.e., with the aid of a stereo vision. Thus, our memory stores a 3D information about his or her face configuration and we utilise the same for recognising his or her facial images. However, the problem is quite different when we are asked to visually compare two face photographs for identity establishment. Even though, the retinal images in both the eyes are identical in case of viewing a 2D facial image, the distribution of shades provokes us to imagine an approximate 3D face configuration with the aid of a subjective consideration of our experience on viewing live human faces. But, accuracy and adequacy of such an approximate 3D reconstruction may not escape unquestioned. For example, when for the first time we view someone personally (say a VIP), whom we have seen earlier only in photographs, we often have a new experience about his or her facial appearance, i.e., our old knowledge regarding his or her face configuration based on photograph viewing, did not provide us with an error-free 3D perception. Thus, human recognition of a questioned facial image with the aid of a comparable standard can utilise a little of subjectively reconstructed 3D information and so the human identification process in such a problem is primarily based on a 2D comparison of images. However, the shade distribution in the images does assist us in the recognition process in some other way. While dealing with the identity problem of facial images, like all other identity problems, we spontaneously search for the symmetries of features both locally as well as globally. Some facial features are well-defined with sharp edges, while some are unsharp or ill-defined. The information contained in shade distribution plays a major role in the detection process of ill-defined or ambiguous features which we perceive by a subjective analysis. It is worth noting that the symmetry that we explore in visual recognition of facial images has a special characteristic. While we can comfortably identify nearly front view facial images, we often fail to recognise poorly angulated or oblique face views. This failure cannot but be attributed to lack of proper symmetry, i.e., the symmetry analyzed by our reflex mechanism is an approximate one which ceases to exist when the facial images are not nearly front view ones. Or, in other words, the inclined face views, which show up more 3D aspects of face configuration than nearly coplanar front view features, do not manifest the symmetry analyzed by our visual perception, It happens because of our inability to form a proper 3D perception from the shade distribution as noted already. Due to such a limitation of our visual perception of facial images, it has because an accepted convention that an official identity photograph should always be a front view one so as to ensure an easy visual recognition. Broken projective symmetry exhibited by human face photographs has exactly similar characteristics as above, i.e., it is good enough for identification purposes in case of nearly front view facial images, but badly broken and as such unsuitable for identification of face views inclined by more than 30 degrees from normal front face view [9]. It is so, because front view facial features are approximately coplanar and thus nearly invariant under transformations of projective symmetry group. On the other hand,

P. Sinha / Forensic Science International 98 (1998) 67 – 89

71

oblique face views exhibiting non-coplanar facial aspects fail to manifest invariance under projective transformations. This striking resemblance of broken projective symmetry with that analyzed by our visual perception appears stimulating and so, broken projective symmetry is worth exploring for modelling the human symmetry perception process and we may suitably utilise group theoretical tools in order to design an artificial neural network with a built-in symmetry perception mechanism for dealing with the problem of recognising nearly front view facial images. In fact, group theoretical models of brain function are among the earliest studies in the theory of neural networks [12,13]. The subjective analysis involved in human perception for detection of ambiguous or ill-defined features may also be artificially implemented by using so called fuzzy logic. It is known that although fuzzy processing deals with imprecise data, such processing is done in a precise and well defined way which eludes human-like errors in subjective analysis of ambiguous information. So, a robust character can be invoked in the neural network by resorting to a fuzzy analysis of ambiguous data concerning ill-defined facial features and thus, the information contained even in ill-defined features may be utilised by the machine as done subjectively in human recognition process. The designing of such an artificial neural network appears in the following section.

3. A robust neural network for symmetry perception A symmetry perceiving adaptive neuronet (SPAN) has been designed for facial image recognition according to the guidelines elaborated in the last section. It has been attempted to effectively utilise the machine-advantage complemented by human expertise – the present practical need being attributed priority over attempting for total automation. The pair of images to be compared should be presented to SPAN as source (input) and target images. SPAN adapts its link weights by a supervised learning that requires inputting a feature subset of the source image and an associated feature subset of the target image as training examples. The trained or adapted SPAN processes the source image so as to make it superimposable over the target one. In the proposed method, the feature selection for training and the final examination of matching exhibited by machine-made superimposed images are to be done by human skill, since the machineability in this regard has not yet achieved human-like perfection. On the other hand, we explore the machine-advantage for getting one of the images processed and superimposed over the other, because such processes are beyond human capability. Thus, SPAN works in an interactive environment according to the following process, the technical details of which appear in Appendix B. The training of SPAN needs supplying paired examples of associated features from the source and the target images. If we select a particular feature on the source image as a unique pixel and try to associate it with the corresponding feature on the target image, it becomes extremely difficult to locate a unique pixel with certainty due to pictorial ambiguity. As such, it would be advantageous if we could fix a prospective zone or a cluster of pixels instead of a definite pixel. SPAN allows selecting a rectangular area for the associated target feature and it should be so done that the selected zone does not

72

P. Sinha / Forensic Science International 98 (1998) 67 – 89

exclude the correct target feature point associated with the uniquely fixed source feature. Such selections of associated target features for training purpose, amounts to feeding the neural network with ambiguous or fuzzy data. So, for dealing with such training data, we must frame a robust learning algorithm, that would be an artificial implementation of human-like subjective analysis of ill-defined features. It is worth noting that even though unique pixels are to be selected as source features, those need not be confined to geometrically well defined feature points with sharp edges, since there is enough freedom to fix the target association. For example, we may fix a suitable pixel on the right / left malar region as the point of malar prominence. Now, even if such a fixation is erratic according to anthroposcopic characterisation. we can always correctly fix its target association by a suitable rectangular zone that does not exclude the point corresponding to the feature already fixed on the source image. This flexibility allows us to select a good number of training features distributed all over the face region as well as to deal with photographs of poor quality. A supervised training of SPAN is done step by step. Each step of the robust learning procedure involves adjusting its link weights followed by partial defuzzification of the fuzzy target features, i.e., reduction of size of the ambiguous rectangular target feature zones to smaller ones in search of correct target feature points which we failed to identify in our ambiguous selection. Such steps are continued until the ambiguous target feature zones are so squized that both horizontal and vertical dimensions of all the fuzzy target features are reduced to such values which are substantially less than the picture resolution limit, i.e., one pixel width. This limiting dimension has been set at quarter of a pixel width and when such a point is reached, the centroids of the so squized fuzzy target features may be taken as completely defuzzified target features for practical purposes. Then the final weight adaptation of SPAN is done: and this corresponds to convergence of the training. The defuzzification rule, elaborated in Appendix B, implements a robust and self deterministic decision making character of SPAN. SPAN learns the symmetry relation between the source and the target images, taking it for granted that such a relation exists. When the complete source image is presented to the trained SPAN, it responds by outputting the superimposable source image and the nearly coplanar front view facial features of the source image are retained invariant by the processing which is a transformation of the projective symmetry group. For an identity case, the decision of SPAN on source–target association is closely accurate. The larger is the number of training features, the more accurate will be the decision of SPAN on source–target association and a better network learning. As SPAN does not restrict the selection of training features only to geometrically well-defined points with sharp edges, it is always possible to consider a good number of input features for training. In practice, the training of SPAN converges very fast, but a convergence does not necessarily amount to a successful training. If after convergence, each of the SPAN outputs, in response to inputs of training source features, belong to the fuzzy target feature sets selected originally, the training may be called a successful one. An unsuccessful training means a case of non-identity, since, the symmetry model based SPAN is not supposed to work for source and target facial images belonging to different individuals, which are not connected by any transformation belonging to the projective

P. Sinha / Forensic Science International 98 (1998) 67 – 89

73

symmetry group, i.e., SPAN refuses to agree on a symmetry relation between such source and target images. Obviously, in such a case the total source image need not be presented to the adapted SPAN for making it superimposable over the target image. Again, a successful training alone cannot warrant an identity of source and target images since, training feature sets were only subsets of the source and the target images. At the same time, fuzzy target features selected for training might have had such large width / height that even incorrectly output source features belonged to the fuzzy target feature sets. In any case, for a successful training the total source image must be presented to the adapted SPAN for processing, so that the final SPAN output may be superimposed over the target image. The superimposed / composite images, produced subsequently, will allow visual examination of featurewise as well as holistic matching and final decision on identity should be made by resorting to the forensic anthropologist’s expertise, which could not be exercised with the original source and target images before processing by SPAN. A software for implementing SEAN in a PC environment has been developed in C and compiled by Turbo C (version 2.0) compiler, the ‘graphics.lib’ of which has been linked in the programme. The present version of SPAN accepts image files in PCX formats only and, as SPAN has to deal with two different image files simultaneously, a combined colour cum grey palette with 6(R)36(G)36(B)5216 RGB colours and 40 grey levels (total 256 pixel values) has been fixed for dealing with both colour as well as black and white images. The SPAN output image is saved in PCX format with this fixed palette. SPAN can be run in three resolution modes, viz., (i) medium (6403480), (ii) high (8003600) and (iii) super (10243768) depending on hardware capability. The interactive feature selection for the training of SPAN is done by placing a graphic cursor on the desired pixel for the source features, while by dragging rectangles for the associated fuzzy target features. For comparing SPAN output images with the SPAN target images a separate software, viz, SPANVIEW has been developed having the same fixed palette and selectable resolution modes. SPANVIEW incorporates some standard graphics editing functions to assist effective use of its main functions. For producing composite images, SPANVIEW has five functions, viz, overlay, superimpose, blockcombination, horizontal strip-combination and vertical strip-combination. Apart from such one step functions, a dynamic sweep function has also been included in SPANVIEW for an easy feature-wise comparison. When this function is operated, a processed source image sweeps over the corresponding target image or vice versa at interactively-controlled speed along any desired direction, viz, (i) left to right, (ii) right to left, (iii) top to bottom and (iv) bottom to top. Sweeping can be stopped at any desired position and the resultant composite image with a horizontal or vertical line of demarcation over any particular feature may be saved for demonstration of feature-wise matching or mismatching. There is yet another novel way of examining and demonstrating superimposition. This may be done by printing the images to be superimposed on transparency sheets. Then the overlaid sheets may be viewed either directly against light or through an overhead projector. Such enlarged projections provide an excellent examination cum demonstration facility. A video projector may also serve the same purpose but the former procedure is much more cost effective. The programmes SPAN and SPANVIEW were run in two different machines for the

P. Sinha / Forensic Science International 98 (1998) 67 – 89

74

presently cited applications. The first machine was a 33 MHz PC-AT 486 DX2 with 8MB RAM and a colour VGA monitor, which allowed a resolution up to the high resolution mode. All the three resolution modes could be accessed in the second machine which was a 100 MHz Pentium with 16MB RAM and a colour SVGA monitor. Even in the slower machine, the processing time was negligible in comparison with the time involved in the interactive feature selection process. This is so because the symmetry model based SPAN has a simple architecture with a small number of processing units and the training converges extremely fast. Again, the mapping function estimated by SPAN being a simple one, the response time of adapted SPAN is also very short.

4. Applications The best way to test the performance of SPAN is to examine simulated cases of identity with apparently dissimilar facial images; as well as cases of non-identity with facial images having close resemblance. Cases of identity with facial images changed by both artificial disguise and natural aging will be considered first. In order to collect test images of human faces, artificially disguised with a good perfection, we have resorted to images of actors and actresses in movies where they play a variety of roles with different make-ups carefully done by professional make-up men. For example, actress ZA (vide Fig. 1a) has been disguised as a man with beard and moustache in a movie as shown in Fig. 1b. Fig. 1a and 1b were input to SPAN as source and target images respectively. Ten training features were selected in this case, which were four corners of eyes, mid-nasal and sub-nasal points, two points of malar

Fig. 1. Comparison of disguised facial image of actress ZA with her normal face by SPAN.

P. Sinha / Forensic Science International 98 (1998) 67 – 89

75

prominence and two cheilion points. The training successfully converged in six epochs only. When Fig. 1a was presented to the trained SPAN, the output was as shown in Fig. 1f, which is superimposable over 1b. It is interesting to note that unlike Fig. 1b, Fig. 1a and 1f appear to have similar looks in respect of face orientation or angle of projection, as the characteristics of shade distribution and lighting effects have been retained invariant by the symmetry model based SPAN. In fact, there is no doubt that facial features are differently projected in Fig. 1a and 1b. But, these features are mapped similarly in Fig. 1b and 1f, even though we visually fail to perceive the same. Such a visual problem is a sort of illusion, which is resolved when we produce composite images from Fig. 1b and 1f for examining their matching. The total superimposition, shown in Fig. 1c, exhibits a holistic matching, while the vertical strip-wise composite image (vide Fig. 1d) demonstrate the continuity of horizontally extending features like, eyebrows, eyes, lip structure etc. Likewise, the horizontal strip-wise combination shown in Fig. 1e exhibits the matching of vertically extending features like nose. A few other composite images with lines of demarcation on different features have been displayed in Fig. 1g, 1h and 1i in order to demonstrate feature-wise matching more clearly. Apart from continuity of well defined features like eyebrows, eyes, nose, lips etc., the smooth curvature continuity in the malar regions is also worth noting. Such disguised facial images of a number of actors and actresses have been successfully compared by SPAN and one more example from these tests deserves citation. Actor SK played as many as eight different roles in a movie under different disguises and such a series of apparently dissimilar facial images of BK were compared among themselves. The results of comparison for three such images from this series have been chosen for demonstration since, these images are not sharp ones and so, the robustness of SPAN may be tested by presenting such images to SPAN. In this example, Fig. 2a, 2b and 2c, having different facial expressions were compared. These images were input to SPAN in two pairs, viz, (2a12c) and (2b12c), 2c being the target image in both the cases. As such, the final SPAN outputs for these two comparisons i.e., Fig. 2d and 2e are both superimposable over the common target 2c and therefore, 2d and 2e are also superimposable over each other. In addition to pair-wise combinations (vide Fig. 2f to 2k) of these three images, i.e., Fig. 2c, 2d and 2e, their triplet combinations have also been made as shown in Fig. 2l to 2q for demonstrating the identity of the three simultaneously. It is interesting to observe that each of the composite images, made out of different pieces from different images, make one complete face without any discontinuity. It is also worth noting that, though the facial expressions in these three images are different, a holistic matching of the faces is not obscured in the pair-wise total superimpositions shown in Fig. 2f, 2g and 2h. The differences in facial expressions have been manifested only in such features which are physically altered. For example, the bulging eyes in 2d and 2e mismatched with the normal eyes in 2c except for the corners of the eyes which matched accurately. Such differences could be clearly seen by sweeping Fig. 2d or 2e over Fig. 2c, rather than in composite images, since the images were of quite poor quality. It may also be noted that the face region in 2b was partially covered. But, such a situation did not pose any serious problem, since the major front view features were visible, though it was difficult to locate unique feature points due to poor image quality. The robust SPAN made proper decision in searching out feature-

76

P. Sinha / Forensic Science International 98 (1998) 67 – 89

Fig. 2. Comparison of three facial images of actor SK with different sorts of artificial make up by SPAN.

wise source–target association for adapting the symmetry relation in such a case with pictorial ambiguity. Thus, we could assess the symmetries effectively, which was not possible by the earlier method [9–11]. Under such circumstances with unsharp / poor facial images, while the fault tolerant SPAN will take care of producing superimposed / composite images, the anthropologist’s expertise plays a critical role in the establishment of identity. It may be recalled at this point that forensic anthropologists are already used to deciding on identity in cases of craniofacial identification by examining superimposed images, where an ambiguity due to soft tissue thickness is always present. Let us next consider comparison of facial images changed due to natural reasons. Fig. 3 of reference [1], presents a series of photographs of an individual at ages ranging from 11 years to 49 years. Apparent dissimilarity was maximum between the facial images of the youngest and the oldest, the comparable portions of which have been reproduced in Fig. 3a and 3b. Fig. 3a and 3b were presented to SPAN as source and target images respectively and Fig. 3c was the final SPAN output after a successful training. Fig. 3d is the total superimposition of Fig. 3b and 3c and some other combinations of these images have been displayed in Fig. 3e, 3f and 3g. As seen clearly from these figures, both holistic and feature-wise matching are so striking that identity cannot be denied.

P. Sinha / Forensic Science International 98 (1998) 67 – 89

77

Fig. 3. Comparison of facial images of an individual at ages of 11 years and 49 years by SPAN (Fig. 3a and 3b have been reproduced from figure 3 of reference [1] with the author’s kind permission).

However, it is true that there was some cranial development of the boy after his 11 years of age, since, cranial growth at this age is normally about 70%. But, the matching shown by SPAN did not indicate an significant change in face configuration. It is so, because the cranial growth after 11 years of age appears nearly a process of pure enlargement keeping the ratios of interfeature distances unaltered, which mathematically corresponds to a mere scale transformation. A scale transformation of any object also induces scale transformations in its perspectives. The group of such scale transformations being a subgroup of the projective symmetry group, such cranial growth did not pose any problem to SPAN to correctly produce superimposed images for identity establishment. At this point, it may also be noted that if there is any sort of perspective deformation or change in aspect ratio during image scanning process, SPAN will automatically take proper care of the same and produce an accurate superimposable image, since all transformations corresponding such deformations belong to the projective symmetry group. Now, we shall consider two cases of non-identity with similar facial appearances for testing the performance of SPAN in this regard. The first one concerns facial images of two ladies who are monozygotic twins as has already been established by anthropometric and anthroposcopic analyses. Fig. 4a and 4b are their facial images taken at the same time and resemblance of their face views is apparent. Fig. 4a and 4b were presented to SPAN as source and target images respectively with nine training features comprised of

78

P. Sinha / Forensic Science International 98 (1998) 67 – 89

Fig. 4. Comparison of facial images of monozygotic twins by SPAN Case 1.

four corners of eyes, mid-nasal and sub-nasal points, two cheilion points and the pogonion. The training was successful, i.e., identity could not be ruled out at the training level. So, Fig. 4a was presented to the trained SPAN and Fig. 4c was the SPAN output, which is superimposable over Fig. 4b. Fig. 4a and 4b show an apparent distinction that the mouth corner fold, as seen in 4a, is absent in 4b. However, a visual comparison of Fig. 4b and 4c reveals a few more differences which were not so apparent when 4b was compared with 4a. First, the hair line boundaries are different. Second, the malar regions are differently pronounced and third, there is some difference in the chin shape. The total superimposition (vide Fig. 4d), however, fails to manifest the difference in the malar region, while the other two above noted differences are visible. The distinction in respect of mouth corner fold is also lost in the total superimposition. It is so because the photographs were taken under identical lighting conditions and as such, they had similar grey level densities which merged in the total superimposition. The vertical and horizontal strip-wise combinations, presented in Fig. 4e and 4f, show the differences more prominently and a new difference has been manifested in Fig. 4e and 4f. It is worth noting that even though the eyes proper match accurately the eye folds below the

P. Sinha / Forensic Science International 98 (1998) 67 – 89

79

orbit disagree. Although the nasal structures show a slight difference (vide Fig. 4f) the mouths do not show any significant distinction. In a human face we are first attracted by the eyes, followed by the nose and the mouth and in the present case these features are so similar that the two images Fig. 4a and 4b look alike. The difference noted in the gonion region in Fig. 4d, 4e and 4f should not be considered for making any decision since, the applicability of SPAN is restricted to the nearly coplanar front view facial features only. Again, the marked difference of eyebrows should not be taken seriously because, those are not natural ones, which were plucked and subsequently drawn artificially. The second case of non-identity also concerns a pair of monozygotic twins who are two young girls and as such their differences are even smaller. Fig. 5a and 5b were the pair of images presented to SPAN as source and target images with the same set of training features as in the earlier case. The training was again successful and Fig. 5c was the final SPAN output when 5a was presented. A first inspection of the two images shows only a difference in respect of chin shape. Incidentally, the hair styles in this case are such that the hair line boundaries are not visible, and so any comparison in this respect could not be done. The total superimposition, shown in Fig. 5d, shows a good holistic matching except for the lower boundary of the chin. The vertical and horizontal strip-wise combinations (vide Fig. 5e and 5f) expose a difference in nasal structure which is particularly prominent at the right alare. The upper lid of the right eye also mismatch by a small amount and in case the eyes in the two figures are in normal full

Fig. 5. Comparison of facial images of monozygotic twins by SPAN Case 2.

80

P. Sinha / Forensic Science International 98 (1998) 67 – 89

open condition, this may be considered as a dissimilarity. A slight difference in lip structure, especially for the lower lip is also visible in Fig. 5e and 5f. In fact, the differences are so small that they can be clearly seen on the monitor screen while one image is swept over another at a very slow speed. The above two comparisons of facial images of monozygotic twins by superimposition suggest that even though such facial images can be distinguished by a careful study, it will not perhaps be possible to establish one to one correspondence between face photographs and skulls of monozygotic twins by usual craniofacial identification through superimposition.

5. Discussions A lot of works on anthroposcopic and anthropometric characteristics of human faces have been conducted by anthropologists for more than a century. On the basis of such characteristics, anthropologists have successfully dealt with cases of race identification, individualisation as well as paternity diagnosis from 1926 onwards and extensively after the Second World War [14,15]. it has also been established that facial characteristics are determined by the underlying cranial configuration and this forms the basis of craniofacial identification [16]. Thus, any variation of facial appearance due to external changes, artificial or natural as it may be, does not alter the basic face configuration. As such, except for rare cases where cranial deformation has taken place, symmetries between two facial images of an individual, with different appearances, are not lost though it is not always visually perceptible. Our visual symmetry perception is so limited because it is psychologically biased. Suppose we are supplied with two facial images of the same person, the first one is with beard and moustache, while the second one is of a clean shaven face. After viewing the first one, when we look at the second one for identity establishment, our reflex mechanism searches for the symmetries and in that process we unconsciously want to find the missing beard and moustache. Due to such psychological bias we often fail to visually assess the facial symmetries in many identity cases, for example, in those cited in the last section – even for the SPAN target and the SPAN output images which match on superimposition. SPAN objectively analyses the symmetries with the aid of the powerful mathematical tool of symmetry groups and assists us to decipher the hidden symmetry by breaking the barrier of bias. In fact, symmetry is the basic philosophy of any identity problem. The nature of symmetry analyzed by our reflex mechanism in the identity problem considered here is not known. However, the discussions in Section 2 may provoke one to guess that this visually perceived symmetry is perhaps somewhat like a broken projective symmetry. In such a case, a set of complex neuron fields in our visual cortex may act like the processing units with special types of signal functions as in SPAN and may be so interlinked. Problems concerning personal identification from identity photographs affixed on credit cards, passports, drivers licences etc., may be comfortably dealt with by SPAN. The matching of facial image of the 11-year-old boy with his totally changed facial appearance at 19 years (vide Fig. 3) suggests that SPAN is also applicable to cases of identification of a missing person who appears after a long time with apparently changed facial appearance. Identification of any questioned face from a video tape on crowd

P. Sinha / Forensic Science International 98 (1998) 67 – 89

81

surveillance is a crucial problem of face recognition in crime cases. Methods based on pattern recognition techniques may search out probable faces from a stored database of facial images of suspected persons, for example, F.A.C.E.S (Facial Analysis Comparison and Elimination System) is one such technique under preparation by the Home Office, U.K. [17]. If a nearly front view questioned facial image can be captured from the video tape, it may be compared by SPAN with facial images of potential suspects for establishment of identity. In such cases the questioned image grabbed from the video tape may be of poor quality with pictorial ambiguity. However, the fault tolerant SPAN will successfully produce superimposed images for the anthropologists examination. In fact, facial image recognition problems of a varied nature may be encountered in crime cases and whenever the questioned and the facial image to be compared with are nearly front view ones, forensic anthropologists will find SPAN as a useful working tool. Some recent works report on comparison of perspective invariant ratios of distances between a few fixed feature points on front view facial images, as an aid to face recognition [18,19]. However, the SPAN output and the SPAN target images allow direct comparison of any sort of anthropometric measurements on front view facial features and there is no need to consider such ratios or any other quantity derived from inter-feature distances for a few fixed features, which offers a restricted comparison only. In conventional neural network approaches towards facial image recognition as adapted by engineers, a model free neural network is trained with a number of control facial images of an individual for recognising him or her in a questioned facial image. A successful training of such a network for recognising one individual requires a large number of control facial images as well as a considerably long learning time. On the contrary, SPAN learns about the symmetry between the single control and the single questioned images for identity establishment and the simple architecture as well as mapping function of SPAN makes it computationally greatly economic. Apart from front view facial images, all sorts of flat impressions / patterns, photographic evidences of which are available, may be easily identified by SPAN. Such patterns / impressions frequently occur as clues in crime cases and may be of widely varied nature, viz, tool marks on flat surfaces, foot / shoe prints, tyre impressions, etc. In cases where the questioned / control patterns or impressions cannot be lifted as such for laboratory examination, their photographic evidences will serve the purpose of identification by SPAN. In this respect SPAN offers ample freedom to the photographer for taking snaps of the patterns / impressions. He needs not attempt to properly align his camera focal plane parallel to the plane of the pattern / impression in order to avoid perspective deformation. Rather, he is free to align his camera in any desired orientation according to his convenience so as to capture maximum details of the impression under the available condition of lighting. Perspective deformations are nothing but projective transformations [20] and SPAN will take proper care of deformed photographs which forget the exact shape and size of the original flat impression / pattern. Microscopic tool marks on flat surfaces, which are commonly identified with the aid of comparison microscope by much effort, are also capable of being easily compared by SPAN provided a suitable arrangement for video micrography is made so that such magnified images may be captured by the computer for being presented to SPAN. In facial image recognition by SPAN, comparison of matching must be confined to

82

P. Sinha / Forensic Science International 98 (1998) 67 – 89

nearly coplanar features of front face view. Thus, one should not draw any conclusion from the observed matching or mismatching of ear, features near gonion or head contour (except for lower boundary of chin) in composite images produced by SPAN. The facial features comparable by SPAN include hairline boundary, forehead, eyebrows, eye lids, eye proper, malar region, nasal structure, mouth, lip structure, chin and its shape as well as a good number of wrinkles. An elaborate list of characteristic facial features suitable for identification has been provided by Iscan [1]. Such features are quite large in number and are suitable for identification of an individual when compared feature-wise as well as holistically. Finally, we would like to discuss another promising area of possible application of SPAN. The capability of SPAN to deal with ambiguous / ill-defined features suggests that it is worth exploring to test the applicability of SPAN in dealing with craniofacial identification problems, which involve an inherent difficulty due to ambiguity caused by soft tissue thickness, while adjusting the position and orientation of the skull by comparing it with the facial image. We have made tests on this problem, with some skull identification cases which were already identified by usual video superimposition as well as corroborated by other evidences. The nearly front view facial image and the cranial image in a roughly similar orientation were presented to SPAN as the target and the source images respectively. The uniquely fixed anatomical landmarks on the source image, i.e., on the skull, were associated with ambiguous rectangular zones on the target, i.e., the facial image, for training. The final superimposed image produced by SPAN provided an excellent comparison facility for the cranial features underlying the above mentioned front view facial features which are nearly coplanar. But, such a straight forward application of SPAN, as in case of facial images, is not supposed to work for examining how the skull contour fits in the face and this is an important aspect of craniofacial identification. However, if in such a direct application of SPAN, the nearly coplanar front view features of the skull fail to match with those on the facial image, non-identity may be confirmed without any further test on contour matching. A complete craniofacial identification, including examination of contour fitting, may be done by SPAN by resorting to a suitable segment-wise processing of the cranial image. Tests on implementing such a procedure are being made to develop a craniofacial identification system that would be economical in respect of (i) manual labour, (ii) processing time as well as (iii) cost of implementation together with the added advantage of the robust character of SPAN which can take care of the ambiguity due to soft tissue thickness. A report on this work will be published soon. In the meantime the author will be pleased to receive photographs or image files in floppy disks of front view human faces or of flat impressions / patterns for getting them compared by SPAN. Such requests should be addressed to the director of the author’s laboratory. Technical details of SPAN have been provided in Appendix B for those interested in developing their own systems.

Acknowledgements The author expresses his sincere gratitude to Prof. A.R. Banerjee, Retd. Professor and Head of the Anthropology Department, Calcutta University, for enlightening discussions

P. Sinha / Forensic Science International 98 (1998) 67 – 89

83

and also for supplying photographs of monozygotic twins. The author is also grateful to Prof. N.V. Iscan, Professor and Chairman, Anthropology Department, Florida Atlantic University, for supplying face photographs cited in Fig. 3, permitting to freely use them and also for his encouraging letter. The author likes to thank Dr. M.K. Kundu and Prof. S.K. Pal of Machine Intelligence Unit, Indian Statistical Institute, Calcutta, for stimulating discussions. Thanks are also due to Dr. N.K. Nag, Director, and Mr. Ajay K. Ghose, Asst. Dir. (Biology Div.), of the author’s laboratory for helpful suggestions. Mr. A.K. Ghose, Liaison Officer of the author’s laboratory, who arranged for collecting disguised facial images of film actors / actresses, deserves special thanks.

Appendix A

Artificial neural network The function of brain or central nervous system of an animal is controlled by the behaviours of densely populated neurons and synapses connecting them so as to form a highly complex network. It has never been demonstrated that the so called brain functions, viz, memory, awareness, intelligence. etc., are possessed by individual nerve cells. As such, Rosenblatt [21] argued that, such properties presumably reside in the organisation and function of the network as a whole. Scientists and engineers have, since then, been greatly attracted by artificial neural networks (NN) and attempted to design a variety of such architectures in order to implement brain-like behaviour in machines. An intelligent brain function is responding to external stimuli. We all associate responses to stimuli or in a broader sense we associate effects with causes. In fact, the total process of correctly responding to stimuli involves a number of intelligent acts like decision making, etc. Another intelligent behaviour of human brain is its learning capability. We learn by changing the state of our brain – we cannot learn without changing – learning usually applies to synaptic changes in the brain. Artificial neural networks are attempts to implement such intelligent behaviours in machines. Besides their applicability in creative hardware implementation, artificial neural networks have also emerged as a powerful tool for solving computational problems. In a neurocomputing paradigm, biological neurons are abstracted as processing units which receive / transmit information either from / to other processing units through links like biological synapses or from / to outside. The output from a unit is a function of all the inputs received by it and when the same is transmitted to other units through interconnecting links, gets associated with appropriate weights, called link weights. Thus, the same output from one unit is weighted differently for being input to different destination units. Units of a NN which receive input from outside are known as input units, while those transmitting output to outside are called output units. Processing units which are neither input nor output are termed as hidden units. Like biological synapses, links may either be excitatory or inhibitory depending on whether the link weight tends to increase or decrease the output from the source unit during its transition to the destination unit. The states of output functions of the processing units of a NN and the links

84

P. Sinha / Forensic Science International 98 (1998) 67 – 89

connecting them, determine the state of the network as a whole. A NN is capable of changing its state with time and such a process amounts to adaptation or learning. Thus, the learning procedure of a NN involves adjusting its state. In course of a supervised training, a NN is presented with paired examples of inputs and associated targets. In response, the NN adjusts the values of its link weights in successive steps, called epochs of training. The NN may either update all the link weights simultaneously in each epoch or may do so one by one. A successful training of a NN may require a large number of repeated attempts or training epochs. When the increment or decrement to the link weights during their updating assumes a prescribed limiting value the training is said to have converged. The adapted NN responds to the inputs of training examples by producing such outputs as the associated targets of training examples. A trained NN will correctly respond to prototypes of inputs of training examples. Artificial neural networks have far reaching potential for different types of applications which demand different architecture designs and different learning procedures as well. This new scientific discipline is a fast-growing one and a large number of text books on recent developments in this area are already available.

Appendix B

The architecture and learning algorithm of SPAN The architecture of three layered SPAN is very simple, having only a small number of processing units (vide Fig. 6). Apart from a bias unit the input layer consists of two units for x and y inputs corresponding to co-ordinates of pixels on 2D images. The single hidden layer also has three processing units which are fully connected to the units of input layer with link weights [w i j ] of which w 3 3 is fixed as unity. The hidden units act like simple adaline units with real value output and a vanishing threshold, There are two units in the output layer, corresponding to x and y outputs. The first two hidden units and the two output units have one to one link, while the third hidden unit is connected to both the output units as shown in Fig. 6. All the link weights of hidden to output connections are fixed as unity. The signal function of the output unit (one / two) is to scale down the input received from hidden unit (one / two) by a factor of that received from the third hidden unit. Thus, SPAN estimates a 2D to 2D mapping function of input pixel co-ordinates (x, y) as follows. x output 5 f(x, y) 5 (w 11 x 1 w 12 y 1 w 13 ) /(w 31 x 1 w 32 y 1 1)

(1a)

y output 5 g(x, y) 5 (w 21 x 1 w 22 y 1 w 23 ) /(w 31 x 1 w 32 y 1 1)

(1b)

It is clear that such a model based neural network acts like an adaptive projective transformation filter. The learning procedure of SPAN has essentially the following steps.

P. Sinha / Forensic Science International 98 (1998) 67 – 89

85

Fig. 6. The architecture of SPAN.

Step 1. Preparation of input data The inputs to SPAN for its training are associated feature subsets of source and target images. First a number of feature points on the source image are to be selected as a set of unique pixels hx, y); ´ source imagej. However, the associated target feature subset may not be selected as a set of unique pixels due to pictorial ambiguity arising from various reasons. So, in order to avoid any human error due to ambiguity, we would select a prospective rectangular zone, i.e., a rectangular array of pixels on target image with diagonally opposite corners (x 1 , y 1 ) and (x 2 , y 2 ) (say x 2 .x 1 and y 2 .y 1 ) corresponding to each source feature and leave the ambiguous information with SPAN for necessary analysis and taking proper decision in this regard. Thus, each crisp source feature data (unique point) will be associated with a fuzzy feature set h(x, y); x 1 ,x,x 2 , y 1 ,y,y 2 j (ambiguous rectangular zone) and so, the associated feature subset of the target image will be a set of such fuzzy feature sets. For preparing input training data from features so selected, the origin of the co-ordinate frame of the source image is first translated to the centroid of the source feature subset in order to minimise the effects of projective symmetry breaking as noted earlier [9]. Each fuzzy target feature is then temporarily defuzzified by taking the centroid as a crisp target feature, i.e., a crisp feature data (X, Y) is extracted from the fuzzy feature set h(x, y); x 1 ,x,x 2 , y 1 ,y,y 2 j such that X5(x 1 1x 2 ) / 2 and Y5( y 1 1

P. Sinha / Forensic Science International 98 (1998) 67 – 89

86

y 2 ) / 2. The set of crisp target features, so extracted, is also translated to the target frame as done for source features due to same reasons. Now, any such crisp target feature, extracted from an ambiguous information, cannot have its truth value equal to 1. The ambiguity for which a rectangular feature zone was selected may arise – from different reasons like variation in shade distribution depending on lighting condition during photographing, unsharp camera focusing, poor image quality, etc. So, the cause of ambiguity and hence its nature may vary from one image to another and even from one feature to another for the same image. Thus, we are not in a position to construct a unique membership function that would be valid for all sorts of fuzzy feature sets, so as to ascertain the membership value of the crisp data (X, Y) in any fuzzy feature set that we may encounter with in any practical situation, Anyway, we may go for an averaging procedure with the conjecture that the sum of truth values of all the nixels contained in the rectangular array is unity, i.e., the rectangular zone has been so selected as to include the correct feature point that should be associated with the corresponding source feature point. In practice, the rectangular arrays chosen for different features may have different heights and widths. Again, the x-uncertainty and the y-uncertainty of the same feature may also differ. For example, a target feature fixed by a vertically extending thin rectangular zone would have a very small x-uncertainty, while the y-uncertainty is not so. We must take suitable care that SPAN does not miss such information during its analysis of the fuzzy data. We, therefore, should assign individual truth values to X and Y, instead of a single truth value to the pixel (X, Y). Now, in the fuzzy feature set h(x, y); x 1 ,x,x 2 , y 1 ,y,y 2 j, (x 2 2x 1 ) and ( y 2 2y 1 ) are measures of x and y uncertainties respectively. We attribute average truth values ‘u’ and ‘v’ to X and Y respectively such that, u 5 1 / [1 1 (x 2 2 x 1 )]

(2a)

v 5 1 / [1 1 ( y 2 2 y 1 )]

(2b)

The resultant truth value of the pixel (X, Y) will be given by the product (u.v). Obviously, had a target feature been fixed by a unique pixel, i.e., x 1 5x 2 5X, then both the individual X and Y truth values as well as that of the pixel (X, Y) would have been unity. The source feature subset, the associated (temporarily defuzzified) crisp target feature subset along with the individual X, Y truth values comprise of the total training data for SPAN. Step 2. Computation of link weights The link weights [w ij ] are to be so computed as to minimise the function, F(w ij ) 5

O

[( f(x i , y i ) 2 Xi )2 1 ( g(x i , y i ) 2 Yi )2 ] ,

(3a)

151,N

where N is the number of training features. Now, the uncertainties involved in the selection of different features are different and so are the truth values. The feature selected with greater certainty should be given more favouritism during minimisation.

P. Sinha / Forensic Science International 98 (1998) 67 – 89

87

This may be implemented by associating the truth values as weight factors with the two terms in ,FDR.3a, / FDR.. Which should now look like, F(w ij 5

O [h(u .( f(x , y ) 2 X )j 1 hv .( g(x , y ) 2 Y )j ] . 2

i

1

i

i

2

i

i

i

i

i 51,N

It may be noted that the derivatives of F(w i j ) with respect to w i j are linear functions of w i j . As such, a straightforward application of the method of least square fit is most suitable for minimisation in this case. Apart from faster weight adaptation than iterative methods, this has the major advantage of eluding possible local minima. However, the weights so adapted are not final, since, the choice of centroids of fuzzy target features as defuzzified crisp features was only a temporary one and may involve errors. The final weight adaptation will be made only when the error involved in the process of defuzzification is reduced to a prescribed limit which must be much smaller than the picture resolution value, i.e., a single pixel width. Step 3. Updating fuzzy target features In step 2. all the training features were simultaneously considered for finding the best fitting set of link weights. Such a weight adaptation will help us to frame a defuzzification rule that will characterise SPAN with a self deterministic decision making capability for searching out the associated target feature points from the fuzzy or ambiguous data. Let us assume that, (i) there exists a projective symmetry between the source and the target images and (ii) the training features are large in number and distributed all over the face region so that the errors involved in the supplied target feature data (temporarily defuzzified) have a random distribution. In such an ideal situation, the method of least square fit will yield error-free solutions for the set of link weights. Hence, with such link weight adaptation the neural network will respond to inputs of training source features by outputting the points of their correct target association, which we failed to identify in our ambiguous selection. Thus, we may reasonably infer that, in reality, the network outputs for input training data on source image, should be near about the error free target feature points for a good number of training features in a case of identity which ensures existence of projective symmetry. Let a rectangle ABCD represent a fuzzy target feature zone associated with a particular source feature point and its centroid P was temporarily used as the crisp target association with that source feature for link weight adaptation (vide Fig. 7). If O be the corresponding network output after link weight adaptation, O must lie closer to the unknown correct target feature point as compared to P. Therefore, we may approach towards an error free crisp target association by shifting the same from P along the vector PO. But, in reality, we have not yet acquired a definite knowledge about the exact location of the crisp target feature that we are searching for. As such, we should not shift it from P directly to O, rather it would be judicious to update the fuzzy target feature zone ABCD by the smaller rectangle with P and O as diagonally opposite corners, because of reasons as follows. First, the crisp target feature that should be input during the next training epoch will be shifted from P to the centroid of the smaller rectangle, i.e., to O. Thus, the shift vector of the crisp feature,

88

P. Sinha / Forensic Science International 98 (1998) 67 – 89

Fig. 7. Successive steps of defuzzification of fuzzy target features (rectangular zones).

PQ5(1 / 2).PO has a reasonable magnitude along a nearly right direction. Second, the vector PO may be regarded as an approximate measure of the error involved in selection of P as the crisp target feature. Thus, the less would be the error involved in fixing P, i.e., the smaller PO would be, the larger would be the average truth value associated with the updated fuzzy target feature. Such successive updatings will defuzzify the target feature step by step and in this way we shall gradually approach towards an error free unambiguous source–target association. It may be mentioned that the updating procedure should take into account one more point. It is clear from Eqs. (1a) and (1b) that, the origin of the source image is mapped on to the point (w 1 3 , w 2 3 ) instead of the target origin. In order to ensure origin to origin mapping for reasons noted in step 2. the target origin should be translated to the point (w 1 3 , w 2 3 ) during each updating. Step 4. Convergence check The truth values of updated fuzzy target features should be computed as done in step 1. If the lowest of both X, V truth values is greater than 0.8, i.e., both the x and y uncertainties of all the updated rectangular target feature zones are less than quarter of a pixel width, the training may be considered to have converged. Otherwise, the updated target feature data along with the unaltered source feature data should be fed back to step 2. In case of convergence the centroids of the finally updated fuzzy target features may be taken as completely defuzzified crisp target features for practical purposes since, both the x- and y-uncertainties are substantially less than the picture resolution limit, i.e., one pixel width. The final weight adaptation is done by associating the defuzzified target feature data with the unique source features and then minimising Eq. (3a).

P. Sinha / Forensic Science International 98 (1998) 67 – 89

89

In practice, while selecting the fuzzy target features, i.e., the rectangular zones, a user normally attempts to fix each rectangle centred around the visually guessed target feature point associated with the corresponding source feature point. Thus, the distribution of errors in the first temporary defuzzification should not deviate much from a random distribution. The iterative defuzzification procedure takes care of such deviations and thus, a careful feature selection leads to a closely accurate convergence of network learning, so that the possible error involved during response of trained SPAN to an input image is much less than the picture resolution limit.

References [1] M.Y. Iscan, Introduction to techniques for photographic comparison: potentials and problems, in: M.Y. Iscan, R.P. Helmer (Eds.), Forensic Analysis of the Skull, Wiley-Liss, 1993, pp. 57–70. [2] R. Chellappa, C.L. Wilson, S. Sirohey, Human and machine recognition of faces: a survey, Proc. IEEE 83 (1995) 705–740. [3] M.A. Turk, A.P. Pentland, Face recognition using eigenfaces, Proc. Int. Conf. on Patt. Recog. (1991) 536–591. [4] A. Pentland, B. Moghaddam, T. Starner, M. Turk, View based and modular eigenspaces for face recognition, Proc. IEEE Computer Soc. Conf. on Computer vision and Patt. Recog. (1994) 84–91. [5] B.S. Manjunath, P. Chellappa, C.V.D. Malsburg, A feature based approach to face recognition, Proc. IEEE. Computer Soc. Conf. on Computer vision and Patt. Recog. (1992) 373–378. [6] G.J. Kaufman Jr., K.J. Breeding, The automatic recognition of human faces from profile silhouettes, IEEE Trans, Syst. Man. and Cybern. vol. SMC- 6 (1976) 113–121. [7] T. Kohonen, Self Organisation and Associative Memory, Springer, Berlin, 1988. [8] T.B. Stonham, Practical face recognition and verification with WISARD, in: H.D. Ellis, M.A. Jeeves, F. Newcombe, A. Young (Eds.), Aspects of Face Processing, Nijhoff, Dordrecht, 1981, pp. 426–441. [9] T. Majumdar, P. Sinha, Photographs of the human face and broken projective symmetry, J. Forens. Sci. Soc. 29 (1989) 381–395. [10] P. Sinha, Recognition of changed facial appearance with the aid of a facial image recognition system, Police Research and Development (BPR&D, Ministry of Home Affairs, Govt. of India). Jan–Mar (1995) 37–41. [11] P. Sinha, Symmetry sensing through computer vision and a facial image recognition system, Forens. Sci. Int. 77 (1996) 27–36. [12] R. Lenz, Group theoretical methods in image processing, in: G. Goos, H. Hartnanis (Eds.), Lecture notes in Computer Science 413, Springer-Verlag, 1987. [13] W. Pitts, W.S. McCulloch, How we know Universals: the perception of auditory and visual forms, Bull. Math. Biophys. 9 (1917) 127–147. [14] H. Schade, Vaterschaftsbegutachtung, E. Schweizerbart’s che Verlagsbuchhandlung, Stuttgart, 1954. [15] R. Martin, K. SaIler, Lehrbuch der Anthropologic, I and II, Gustav Fischer Verlag, Stuttgart, 1957. [16] W.M. Krogman, M.V. Iscan, The Human Skeleton in Forensic Medicine, C. Thomas, Springfield IL, 1966. [17] P.J. Benneth, Facial identification techniques, in: Speakers Notes 9532, The British Council International Seminars on Advancing the Scientific Investigation of Crime, Durham, July, 1995. [18] T. Catterick, Facial measurements as an aid to recognition, Forens. Sci. Int. 56 (1992) 23–27. [19] M.S. Kamel, H.C. Shen, A.K.C. Wong, T.M. Hong, R.I. Compeanu, Face recognition using perspective invariant features, Pattern Recog. Lett. 15 (1994) 877–883. [20] P. Sinha, Photographs of flat impressions and their projective symmetry, J. Forens. Sci. Soc. 28 (1988) 79–86. [21] F. Rosenblatt, Principles of Neurodynamics, Spartan Books, Washington DC, 1962.