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Cost-effective solid reconstruction from an X-ray image
Journal of Materials Processing Technology 121 (2002) 207–216
Cost-effective solid reconstruction from an X-ray image Simon S.P. Shuma, W.S. Laub, Matthew M.F. Yuenc, K.M. Yua,* a
Department of Manufacturing Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong b Hong Kong Institute of Vocational Education (Chai Wan), 30 Shing Tai Road, Chai Wan, Hong Kong c Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clearwater Bay, Hong Kong Received 17 October 2000
Abstract Solid reconstruction of a 3D computer solid model from 2D line drawings has been studied widely over the last two decades. In fact, it is one critical operation in the rapid reverse engineering of a mechanical part. The computer model reconstructed can be used in down-stream operations such as part re-design, engineering analysis, rapid prototyping or CAM. For industrial application, the method should be efficient, cost effective, with minimum human interaction, and reasonably accurate. A new method is studied and implemented using a computer-vision approach to extract information from a mechanical part and generate the corresponding computer model. The method takes advantage of X-rays to capture images of an object with obscured interior details. The reconstruction algorithm will generate an information-complete solid model. The paper explains and discusses the method with examples and explores its cost effectiveness. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Solid reconstruction; Reverse engineering; Computer vision; X-rays
1. Introduction In reverse engineering, the information being extracted from a physical object is transformed into solid models, from which computer-aided engineering (CAE) analysis and computer-aided manufacturing (CAM) techniques can be used. While it is a simple concept, reverse engineering can be used for many purposes. For instance, it may be necessary to produce a spare part when no original drawings or specifications of a component are available. It may also be necessary to modify the design of such a part. In these cases, a geometric model is required to verify new uses and modifications. Currently, computer vision is one powerful method used in reverse engineering. Computer vision has been studied so as to be able to use computer systems to recognize character figures, photographs, 3D objects, remote sensing data, etc. Decades of effort from the research community has resulted in a variety of techniques to infer 3D structures using information encoded in images, such as depth, surface orientation and the distance of an object from the viewer. Such techniques are stereo-imaging, shape from X (X can be shading, photometric stereo, texture, focus/defocus and motion), range imaging and recognition from line drawings, from which they provide information about the layout of visible surfaces. * Corresponding author. Tel.: þ852-2766-6603; fax: þ852-2362-5267. E-mail address: [email protected] (K.M. Yu).
Among various computer-vision methods, line drawings are commonly employed to represent the 3D shape of objects. From the view point of a computer, line drawings are simply a collection of 2D line segments and therefore an intelligent mechanism is required to extract 3D information from them and to reconstruct the corresponding solid. This has been one of the main areas of research in fields such as scene analysis, picture interpretation and computer vision. Probably the earliest attempt at machine interpretation of line drawings can be found in Roberts’ system [1] in 1965. Given a single-view image of an object taken from a certain number of prototypes, his system identifies the object by first extracting a line drawing from the image and then searching for a prototype of which the projection coincides with the line drawing. Next, Huffman [2] and Clowes [3] proposed a systematic method to interpret polyhedral line drawings based on vertex and edge configurations in a single-view by a labeling scheme. The interpretation method was further developed by Falk [4], Shirai et al. [5], Winston [6], Ballard and Brown [7], Sugihara [8] and other researchers. On the other hand, Idesawa [9] was the first to reconstruct 3D models from 2D line drawings of multiple views. Markowsky and Wesley [10,11] constructed all polyhedral objects from the same wire-frame which results in a huge number of solutions. Haralick and Queeney [12], Aldefeld [13], Bin [14], Gujar and Nagendra [15], You and Yang [16], Tanaka et al. [17] and Shin and Shin [18] extended Markowsky and Wesley’s work and developed more efficient, precise and robust algorithms with a wider input geometric domain.
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In summary, the single-view approaches perform interpretation rather than reconstruction. On the other hand, the multiple-view approaches are able to generate a 3D model. Multiple-view approaches are more useful because they provide the depth information. Orthogonal projections are usually needed in the reconstruction from which the description of line drawings is normally unambiguous.
2. Solid reconstruction method The current research is concerned mainly with the reverse engineering of polyhedral objects using a two-stage extrusion which is able to construct a solid from 2D line drawings of multiple orthographic views. The first step is image acquisition. In general, images are considered to be formed by incident light in the visible spectrum falling on a partially reflective, partially absorptive surface, with the scattered photons being gathered up in a camera lens and converted to electrical signals either by vacuum tube or charge-coupled devices (CCD). In practice, this is only one of the many ways in which images can be generated. Thermal, ultrasonic, Xray and other techniques can all generate images. Here, the pre-processing of line drawings has resorted to image acquisition by the X-ray approach. An X-ray apparatus is used to capture images of a physical object from multiple views. CorelDRAW is used as an image processing software for converting the raster images to line drawings. An AutoLISP program has also been written to construct the 3D solid from 2D line drawings. 2.1. Image acquisition Fig. 1 shows the work flow of the reverse engineering a physical object. Although the use of a CCD digital camera allows most of visible light images of a polyhedral object to be captured in a computer, there are some obscured areas hardly be able to captured by visible light. Since materials are transparent to X-rays, it becomes the most appropriate means to capture a hidden or obscured boundary of an object. Fig. 2 illustrates the detailed steps in which images are acquired by the computer. 2.2. Image processing The low-level conversion of a raster image to vector information is carried out by commercial image processing
Fig. 1. Flow chart of the reverse engineering of a physical object.
software such as Photoshop and CorelDRAW. Photoshop is used to enhance the images, while CorelDRAW is used for raster-to-vector conversion. In high-level processing, the 2D line drawings are first arranged in multiple orthographic views. Finally, a unique 3D CAD model is constructed by a two-stage extrusion method [19]. 2.3. Solid reconstruction The two-stage extrusion algorithm (see Fig. 3) consists of two extrusion stages. In each extrusion stage, geometric entities from only three orthogonal views (say, top, front and right) are used. The entities include both interior and exterior lines in each view. In the first extrusion stage, the contour (i.e. exterior line drawings) in each view is swept along its normal direction according to its respective object dimension. As a result, three extrusion-solids are produced. Intersection of the three extrusion-solids will form a basic-solid.
Fig. 2. Steps in image capture.
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case, the basic-solid will subtract the excess-solid to generate the final 3D solution-solid. The geometric domain covers all 2.5D polyhedral objects, including features of blind holes and/or counter-bore holes. The AutoLISP program implementation is given in Appendix A.
3. Implementation There are three aspects to the implementation of the solid reconstruction method. 3.1. X-ray image capture The X-ray equipment used in the implementation was designed originally for non-destructive testing (see Fig. 4). The images are sensed by X-ray films. An X-ray film consists of a film emulsion containing silver halide crystals coated on a blue-tinted plastic base [20]. After development, the areas that have been exposed to X-rays appear darker than those that were not exposed to X-rays. In the operation, a beam radiation is passed through an object and the transmitted radiation is received on an enclosed X-ray film (see Fig. 5). The intensity transmitted by a given part of the object depends on the nature and thickness of the material through which the radiation has passed. Thus, any geometry of the object may be shown up by differential absorption [21]. During X-ray imaging, calibration is done by putting a standard block gauge near to the object. After film treatment, the radiographic images captured on the X-ray films are directly scanned into gray scale images for image processing. It takes several hours to process the X-ray films and carryout the scanning.
Fig. 3. The two-stage extrusion algorithm.
Next, the unused interior entities in each view will pass through a filtering process in which all redundant entities are removed. If all interior entities are discarded during filtering, the second-stage extrusion will be omitted. The basic-solid will be the unique solution-solid. On the other hand, if some interior entities remain after filtering, they will be swept in the second-stage extrusion to form an excess-solid. In this
Fig. 4. X-ray apparatus (the Rigaku 200EG-S3 X-ray system).
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Fig. 5. An X-ray imaging system.
3.2. Image processing Since raster images are simply a collection of pixels, distortion will result if the size of the bitmap is increased or reduced without vectorizing it. Furthermore, the raw images cannot be used directly but should be enhanced prior to solid reconstruction. One solution is to use commercial computer packages such as Adobe Photoshop [22] and CorelDRAW [23] software. Photoshop works well on the early processing
of image filtering and edge detection. In Photoshop, there are a number of operations that can enhance the images, such as orientating the images, removing unwanted areas from images, sharpening edges, extracting edges from the images, etc. Fig. 6 shows a series of image processing operations used. In CorelDRAW, the pre-processed bitmap images are converted into line drawings. The CorelTRACE module (of CorelDRAW) is used to trace the profile geometry from the raster edge pixels. The traced files are then converted into
Fig. 6. Image processing operations used in solid reconstruction: (a) orientating the image; (b) adjusting the pixel value in the image; (c) adjusting all pixel values by brightness/contrast; (d) detecting edges from the image by filter—find edges; (e) tracing the geometry by the centerline method; (f) AutoCAD geometry.
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with their associate vertices in the other views. A Cartesian coordinate system as shown in Fig. 7 is assigned to each view-contour (i.e. exterior line drawings in each view) in order to establish the point correspondence among the line drawings in third angle projection (see Fig. 8).
4. Results 4.1. Example 1 Fig. 7. The coordinate systems for all views.
Fig. 8. Three view-contours with the coordinate system assigned.
2D line drawings (i.e. .dxf format) by the DRAW module (of CorelDRAW). The 2D line drawings will then act as the input for solid reconstruction. 3.3. Solid reconstruction The two-stage extrusion program is written in the AutoLISP programming language. It is used to construct a unique 3D solid from 2D line drawings. Prior to inputting to the program, the correspondences among the six views are defined according to their geometric relationships in the object. As a result, all vertices in one view are consistent
Two examples will be used to demonstrate the proposed solid reconstruction method. Firstly, X-ray images are captured from Object-1 (a steel block: 100:00 mm 60:00 mm 60:00 mmÞ as shown in Fig. 9. The images are processed into line drawings as shown in Fig. 10 with minor human amendment since there are a few perspective distortions in the images. In the processing, three contours are extruded along their normal direction with respect to the object dimensions (i.e. length, width and height) to form three individual extrusion-solids. The three extrusion-solids are then intersected to produce a basic-solid as shown in Fig. 11. In the second stage, the non-redundant interior line drawings are swept to generate two excess-solids which are then subtracted from the basic-solid to form the final solution-solid as shown in Fig. 12. 4.2. Example 2 For the second example, X-ray equipment is used to capture the image of Object-2 (an aluminum block: 51:00 mm 24:90 mm 22:00 mm) which contains one through-hole and two blind holes of different depths, as shown in Fig. 13. The images are processed into line drawings as shown in Fig. 14. The basic-solid is simply formed by extruding the three rectangular contours. Since the interior entities remain after the filtering, they are used in the second-stage extrusion to form two cylindrical
Fig. 9. Three X-ray images of Object-1 arranged in third angle projection.
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Fig. 13. Three X-ray images of Object-2 arranged in third angle projection.
Fig. 10. Line drawings corrected with human interaction.
Fig. 14. Line drawings of Object-2. Fig. 11. The formation of a basic-solid from the extrusion of three contours: (a) the extrusion of three contours; (b) the basic-solid.
excess-solids. Finally, the basic-solid subtracts the two excess-solids to generate the 3D solution-solid, as shown in Fig. 15. Fig. 15. The solution-solid of Object-2.
5. Estimation of accuracy It is difficult to obtain exact dimensions of line drawings from whatever input methods: it will have deviations which usually result from image capturing (Ecap) and solid reconstruction (Esr) (see Fig. 16). The former deviation (Ecap) is mainly due to perspective effect caused by non-parallel projection of X-rays onto the image sensor (see Fig. 5). Further, this error is also due to image processing resulting from the maximum variation of pixel range at the edges of an
image. It is found that the maximum variation is 2 pixels (see Fig. 17) for a Kodak DC120 digital camera of resolution 1280 960. The latter deviation due to solid reconstruction can be negligible (i.e. Esr ¼ 0), since the input line drawings are corrected manually. The accuracy of the method is studied and analyzed for the worst cases in the implementation. Only the overall length, width and height of each workpiece are measured to
Fig. 12. The formation of a solution-solid: (a) the basic-solid; (b) two excess-solids; (c) the solution-solid.
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Fig. 17. An example to show the pixel variation of an image (assume that the maximum error is 2 pixels).
those for the smaller size workpiece (Object-2) are much less significant. Referring to Fig. 5, it is concluded that the perspective distortion can be minimized for a large point source-to-object distance together with a small object-tofilm distance (Table 1).
6. Discussion 6.1. Image acquisition
Fig. 16. Errors due to image capturing (Ecap) and solid reconstruction (Esr).
estimate the accuracy of the input method. The workpieces are prepared by precision machining. The actual sizes of workpieces are as follows: Object-1, 100:00 mm 60:00 mm 60:00 mm (refer to Fig. 9); Object-2, 51:00 mm 24:90 mm 22:00 mm (refer to Fig. 13). It is found that the errors due to the perspective effect for the larger size workpiece (Object-1) are significant while
One of the main problems of image capture in the implementation is the perspective distortion of images. This affects the image quality, which will in turn affect the result of solid reconstruction. Projection is required to be orthographic so that it can represent the true scale size of an object in the reconstruction. However, for the present X-ray equipment, X-rays are emitted from a point source, and thus it inherently has perspective distortion. If the distance between the point source and the object is very large, the incident radiation is nearly a parallel beam. However, due to the inverse-square law, the intensity is decreased. Therefore, the point source should be as far away as practically allowed, so that the amount of distortion is kept small. In addition, the distance between the object and the film should also be small for the same reason.
Table 1 Deviation due to the perspective effect (Ecap) Object-1
Measured length ¼ 106:74 mm 2 pixels ¼ 106:74 mm ð2=1280Þ 195:28 mm ðsince 1280 pixels is equivalent to 195:28 mmÞ ¼ 106:74 0:31 mm ¼ 106:43 mm ðminimumÞ ¼ 107:05 mm ðmaximumÞ Minimum absolute error ¼ 106:43 100:00 ¼ 6:43 mm Maximum absolute error ¼ 107:05 100:00 ¼ 7:05 mm Minimum relative error ¼ ð106:43 100:00Þ=100:00 100% ¼ 6:43% Maximum relative error ¼ ð107:05 100:00Þ=100:00 100% ¼ 7:05%
Object-2
Measured width ¼ 24:71 mm 2 pixels ¼ 24:71 0:31 mm ðuse the same pixel error as aboveÞ ¼ 24:40 mm ðminimumÞ ¼ 25:02 mm ðmaximumÞ Minimum absolute error ¼ 24:40 24:90 ¼ 0:50 mm Maximum absolute error ¼ 25:02 24:90 ¼ 0:12 mm Minimum relative error ¼ ð24:40 24:90Þ=24:90 100% ¼ 2% Maximum relative error ¼ ð25:0224:90Þ=24:90 100% ¼ 0:48%
Average errors of the two examples
Average minimum error ¼ ð6:43 þ 0:50Þ=2 ¼ 3:47 mm Average maximum error ¼ ð7:05 þ 0:12Þ=2 ¼ 3:59 mm Average error ¼ ð6:42 þ 7:05 þ 0:5 þ 0:12Þ=4 ¼ 3:525 mm
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level. The boundaries between the various gray levels thus reveal the geometric information of the object. However, an X-ray is not able to differentiate the line entity clearly if the difference between the thicknesses of two steps is not significant. The use of X-ray films has several shortcomings that can be overcome by employing an electronic image acquisition system. Nowadays, an X-ray detector can be incorporated with the X-ray image converter tube attached to a CCD camera. This technology is more accurate and efficient in image acquisition, but is much more expensive. 6.2. Cost comparison There are many different approaches to capture input data for solid reconstruction. The cost of input is a crucial factor to be considered in selection. To compare the costs of different approaches, the unit costs of relevant items are listed in Table 2. From Table 3, the lowest cost method is to apply the visible image acquisition approach (i), but the input geometric domain cannot cover hidden areas of the object. The setup time and processing time are also short. The proposed approach (ii) of using traditional X-ray imaging can offer a wider input domain, but the cost is six times higher than that for the first approach, the difference being due to the more expensive X-ray equipment. The approach (iii) of using digital X-ray imaging can provide a shorter processing time, but the cost is much higher than that of the second approach. The approach (iv) of using 3D digitizing is expensive, and it is unable to capture the internal information of an object. The outputs are point clouds which cannot be constructed explicitly by the present solid reconstruction methods. The computed tomography (CT) approach (v) is too expensive to be afforded by small- or medium-sized manufacturing industries, even though CT is able to acquire both interior and exterior information of an object precisely and very quickly. The CMM approach (iv) is also expensive. Moreover, this approach cannot be automated for one-off measurement, and the setup time and processing time are very long. Fig. 18. Operations to correct perspective distortion: (a) the original image with inclined lines and distorted circles; (b) selecting the image in horizontal and vertical reference guides; (c) correcting distortion by adjusting the corner points around the edges; (d) the corrected image.
Since perspective effect cannot be eliminated completely, minimum human interaction of the images is employed to correct any ‘‘inclined’’ parallel edges. Photoshop has been used to correct any perspective distortion of images, as shown in Fig. 18. Fortunately, X-ray imaging is unlikely to be affected by surface texture since the image is produced from radiation penetrating the material. In fact, the gray levels of a radiographic image depend on the various material thicknesses of an object. The thicker the material, the lighter is the gray
Table 2 Current unit price in the market (1999) Item
Equipment
A B C D E F G
Diffuse front-light setup 5000 Kodak DC120 digital camera 6390 Photoshop 5680 CorelDRAW 3850 AutoCAD 24960 Rigaku X-ray System with film processing installation 280000 Rich. Seifert DP210 Radioscopic X-ray System with 686500 digital Image Enhancement System VISTAPLUS II 3D digitizer 550000 CT 10000000 Coordinate Measuring Machine (CMM) 700000
H I J
Unit price (HK$)
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Table 3 Cost comparison for different data acquisition approaches Approach
Different data acquisition approaches
Investment (HK$)
Setup time and processing time
i ii iii iv v vi
Visible light image acquisition approach: A þ B þ C þ D þ E Traditional X-ray imaging approach: C þ D þ E þ F Visible light þ digital X-ray imaging approach: C þ D þ E þ G 3D digitizer approach: C þ D þ E þ H CT approach: C þ D þ E þ I CMM approach: E þ J
45880 314490 720990 584490 10034490 724960
45 min 1 day 3h 3h 1h 6h
The two-stage extrusion is also superior to shape from X in terms of accuracy. The former is a high-level processing which constructs information-complete solid model from line drawings, whilst the latter is a low-level processing which only generates an approximate shape from the image.
Acknowledgements This work was supported by a grant from The Hong Kong Polytechnic University (Project No. G-V124).
Appendix A. AutoLISP program for two-stage extrusion Fig. 19. Alternative input methods for solid reconstruction.
Other than the investment cost, the running cost and the maintenance cost for approaches (ii), (iii) and (v) are also considerable. In addition, operation safety rules [24] should be observed stringently during their operations. 6.3. Future work The input of reverse engineering is not necessarily a physical object. Fig. 19 shows two possible input methods for solid reconstruction. The input image can be captured by a sensor (a digital camera or X-ray apparatus) from a physical object, or from scanning old 2D paper drawings or their combinations.
7. Conclusions An original solid reconstruction method has been discussed. The result of solid reconstruction from multiple orthographic views is more accurate and superior to that from single-view object recognition, since the former contains more useful information. However, the input domain of the method is currently confined to polyhedral objects. In addition, 2D line drawings inevitably need to be corrected by human interaction prior to solid reconstruction due to inherent perspective distortion. Nevertheless, the X-ray radiographic images are not affected much by the environmental lighting conditions nor the surface texture of the object.
(defun 2_stage_extrusion() (input 2D line drawings from the three views of top, front, right) (first_stage_extrusion for the boundary entities to form three basic-solids) (filter out redundant interior entities) (if (non-redundant interior entities exist) (second_stage_extrusion for the non-redundant interior entities to form an excess-solid) ;then if (setq excess-solid 1) ;else if ) ;end if (subtract the excess-solid from the basic-solid to produce the solution-solid) ) (defun first_stage_extrusion() (setq i 1) (while view(i) (select 2D line drawings which belong to boundary entities) (form contour area Ai) (sweep contour area Ai along its normal vector) (solid generated is stored in Se(i) as an extrusionsolid) (setq i (þi 1)) ) ;end while (setq j 1) (while (extrusion-solid Se(j)) (intersect extrusion-solid Se(j))
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(solid generated is stored in S3v(TFR) as the basic-solid) (setq j (þj 1)) ) ) (defun second_stage_extrusion() (setq k 1) (while view(k) (select non-redundant entities) (remove non-sense entities) (form the interior region ak) (sweep interior region ak along its normal vector) (solid stored in Se(k) as the interior extrusionsolid) (setq k (þ k 1)) ) (setq l 1) (while Se(l) (intersect Se(l)) (solid stored in S3v(TFR) as the interior excesssolid) (setq l (þ l 1)) ) )
References [1] L.G. Roberts, Machine perception of three-dimensional solids, in: J.T. Tippett, et al. (Eds.), Optical and Electro-optical Information Processing, MIT Press, Cambridge, MA, 1965, pp. 159–197. [2] D.A. Huffman, Impossible objects as nonsense sentences, in: B. Meltzer, D. Michie (Eds.), Machine Intelligence, Vol. 6, Edinburgh University Press, Edinburgh, 1971, pp. 259–323. [3] M.B. Clowes, On seeing things, Artif. Intell. 2 (1) (1971) 79–112. [4] G. Falk, Interpretation of imperfect line data as three-dimensional scene, Artif. Intell. 3 (2) (1972) 101–144.
[5] Y. Shirai, K. Koshikawa, M. Oshima, K. Ikeuchi, Application of 3D models to computer vision, Comput. Graphics 7 (3) (1983) 269–275. [6] P.H. Winston, The Psychology of Computer Vision, McGraw-Hill, New York, 1975. [7] D.H. Ballard, C.M. Brown, Computer Vision, Prentice-Hall, Englewood Cliffs, NJ, 1982. [8] K. Sugihara, Mathematical structures of line drawings of polyhedrons—towards man–machine communication by means of line drawings, IEEE Trans. Pattern Anal. Mach. Intell. 4 (1982) 458–469. [9] M. Idesawa, A system to generate a solid figure from three views, Bull. JSME 16 (1973) 216–225. [10] G. Markowsky, M.A. Wesley, Fleshing out wireframe, IBM J. Res. Dev. 24 (5) (1981) 582–597. [11] G. Markowsky, M.A. Wesley, Fleshing out projections, IBM J. Res. Dev. 25 (6) (1981) 934–954. [12] R.M. Haralick, D. Queeney, Understanding engineering drawings, Comput. Graphics Image Process. 20 (1982) 244–258. [13] B. Aldefeld, On automatic recognition of 3D structures from 2D representations, Comput.-Aid. Des. 15 (2) (1983) 59–64. [14] H. Bin, Inputting constructive solid geometry representations directly from 2D orthographic engineering drawings, Comput.-Aid. Des. 18 (3) (1986) 147–155. [15] U.G. Gujar, I.V. Nagendra, Construction of 3D solid objects from orthographic views, Comput. Graphics 13 (4) (1989) 505–521. [16] C.F. You, S.S. Yang, Reconstruction of curvilinear manifold objects from orthographic views, Comput. Graphics 20 (2) (1996) 275–293. [17] M. Tanaka et al., Decomposition of a 2D assembly drawing into 3D part drawings, Comput.-Aid. Des. 30 (1) (1998) 37–46. [18] B.S. Shin, Y.G. Shin, Fast 3D solid model reconstruction from orthographic views, Comput.-Aid. Des. 30 (1) (1998) 63–76. [19] S.S.P. Shum, Solid reconstruction from orthographic projected line drawings, Ph.D. Thesis, The Hong Kong Polytechnic University, Kowloon, Hong Kong, 1999. [20] Paul, Juhl’s, Essentials of Radiologic Imaging, 6th Edition, Lippincott, Philadelphia, PA, 1993. [21] J.G. Brown, X-rays and their Applications, Plenum Press, New York, 1975. [22] Adobe Systems Incorporated, Adobe Photoshop 4.0 User Guide for Macintosh and Windows, 1996. [23] Corel Corporation, CorelDRAW User Manual, Version 7.0, 1996. [24] X-ray Apparatus—Operation Safety Rules Sheet of the Industrial Centre, The Hong Kong Polytechnic University, Kowloon, Hong Kong.
Cost-effective solid reconstruction from an X-ray image Simon S.P. Shuma, W.S. Laub, Matthew M.F. Yuenc, K.M. Yua,* a
Department of Manufacturing Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong b Hong Kong Institute of Vocational Education (Chai Wan), 30 Shing Tai Road, Chai Wan, Hong Kong c Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clearwater Bay, Hong Kong Received 17 October 2000
Abstract Solid reconstruction of a 3D computer solid model from 2D line drawings has been studied widely over the last two decades. In fact, it is one critical operation in the rapid reverse engineering of a mechanical part. The computer model reconstructed can be used in down-stream operations such as part re-design, engineering analysis, rapid prototyping or CAM. For industrial application, the method should be efficient, cost effective, with minimum human interaction, and reasonably accurate. A new method is studied and implemented using a computer-vision approach to extract information from a mechanical part and generate the corresponding computer model. The method takes advantage of X-rays to capture images of an object with obscured interior details. The reconstruction algorithm will generate an information-complete solid model. The paper explains and discusses the method with examples and explores its cost effectiveness. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Solid reconstruction; Reverse engineering; Computer vision; X-rays
1. Introduction In reverse engineering, the information being extracted from a physical object is transformed into solid models, from which computer-aided engineering (CAE) analysis and computer-aided manufacturing (CAM) techniques can be used. While it is a simple concept, reverse engineering can be used for many purposes. For instance, it may be necessary to produce a spare part when no original drawings or specifications of a component are available. It may also be necessary to modify the design of such a part. In these cases, a geometric model is required to verify new uses and modifications. Currently, computer vision is one powerful method used in reverse engineering. Computer vision has been studied so as to be able to use computer systems to recognize character figures, photographs, 3D objects, remote sensing data, etc. Decades of effort from the research community has resulted in a variety of techniques to infer 3D structures using information encoded in images, such as depth, surface orientation and the distance of an object from the viewer. Such techniques are stereo-imaging, shape from X (X can be shading, photometric stereo, texture, focus/defocus and motion), range imaging and recognition from line drawings, from which they provide information about the layout of visible surfaces. * Corresponding author. Tel.: þ852-2766-6603; fax: þ852-2362-5267. E-mail address: [email protected] (K.M. Yu).
Among various computer-vision methods, line drawings are commonly employed to represent the 3D shape of objects. From the view point of a computer, line drawings are simply a collection of 2D line segments and therefore an intelligent mechanism is required to extract 3D information from them and to reconstruct the corresponding solid. This has been one of the main areas of research in fields such as scene analysis, picture interpretation and computer vision. Probably the earliest attempt at machine interpretation of line drawings can be found in Roberts’ system [1] in 1965. Given a single-view image of an object taken from a certain number of prototypes, his system identifies the object by first extracting a line drawing from the image and then searching for a prototype of which the projection coincides with the line drawing. Next, Huffman [2] and Clowes [3] proposed a systematic method to interpret polyhedral line drawings based on vertex and edge configurations in a single-view by a labeling scheme. The interpretation method was further developed by Falk [4], Shirai et al. [5], Winston [6], Ballard and Brown [7], Sugihara [8] and other researchers. On the other hand, Idesawa [9] was the first to reconstruct 3D models from 2D line drawings of multiple views. Markowsky and Wesley [10,11] constructed all polyhedral objects from the same wire-frame which results in a huge number of solutions. Haralick and Queeney [12], Aldefeld [13], Bin [14], Gujar and Nagendra [15], You and Yang [16], Tanaka et al. [17] and Shin and Shin [18] extended Markowsky and Wesley’s work and developed more efficient, precise and robust algorithms with a wider input geometric domain.
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In summary, the single-view approaches perform interpretation rather than reconstruction. On the other hand, the multiple-view approaches are able to generate a 3D model. Multiple-view approaches are more useful because they provide the depth information. Orthogonal projections are usually needed in the reconstruction from which the description of line drawings is normally unambiguous.
2. Solid reconstruction method The current research is concerned mainly with the reverse engineering of polyhedral objects using a two-stage extrusion which is able to construct a solid from 2D line drawings of multiple orthographic views. The first step is image acquisition. In general, images are considered to be formed by incident light in the visible spectrum falling on a partially reflective, partially absorptive surface, with the scattered photons being gathered up in a camera lens and converted to electrical signals either by vacuum tube or charge-coupled devices (CCD). In practice, this is only one of the many ways in which images can be generated. Thermal, ultrasonic, Xray and other techniques can all generate images. Here, the pre-processing of line drawings has resorted to image acquisition by the X-ray approach. An X-ray apparatus is used to capture images of a physical object from multiple views. CorelDRAW is used as an image processing software for converting the raster images to line drawings. An AutoLISP program has also been written to construct the 3D solid from 2D line drawings. 2.1. Image acquisition Fig. 1 shows the work flow of the reverse engineering a physical object. Although the use of a CCD digital camera allows most of visible light images of a polyhedral object to be captured in a computer, there are some obscured areas hardly be able to captured by visible light. Since materials are transparent to X-rays, it becomes the most appropriate means to capture a hidden or obscured boundary of an object. Fig. 2 illustrates the detailed steps in which images are acquired by the computer. 2.2. Image processing The low-level conversion of a raster image to vector information is carried out by commercial image processing
Fig. 1. Flow chart of the reverse engineering of a physical object.
software such as Photoshop and CorelDRAW. Photoshop is used to enhance the images, while CorelDRAW is used for raster-to-vector conversion. In high-level processing, the 2D line drawings are first arranged in multiple orthographic views. Finally, a unique 3D CAD model is constructed by a two-stage extrusion method [19]. 2.3. Solid reconstruction The two-stage extrusion algorithm (see Fig. 3) consists of two extrusion stages. In each extrusion stage, geometric entities from only three orthogonal views (say, top, front and right) are used. The entities include both interior and exterior lines in each view. In the first extrusion stage, the contour (i.e. exterior line drawings) in each view is swept along its normal direction according to its respective object dimension. As a result, three extrusion-solids are produced. Intersection of the three extrusion-solids will form a basic-solid.
Fig. 2. Steps in image capture.
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case, the basic-solid will subtract the excess-solid to generate the final 3D solution-solid. The geometric domain covers all 2.5D polyhedral objects, including features of blind holes and/or counter-bore holes. The AutoLISP program implementation is given in Appendix A.
3. Implementation There are three aspects to the implementation of the solid reconstruction method. 3.1. X-ray image capture The X-ray equipment used in the implementation was designed originally for non-destructive testing (see Fig. 4). The images are sensed by X-ray films. An X-ray film consists of a film emulsion containing silver halide crystals coated on a blue-tinted plastic base [20]. After development, the areas that have been exposed to X-rays appear darker than those that were not exposed to X-rays. In the operation, a beam radiation is passed through an object and the transmitted radiation is received on an enclosed X-ray film (see Fig. 5). The intensity transmitted by a given part of the object depends on the nature and thickness of the material through which the radiation has passed. Thus, any geometry of the object may be shown up by differential absorption [21]. During X-ray imaging, calibration is done by putting a standard block gauge near to the object. After film treatment, the radiographic images captured on the X-ray films are directly scanned into gray scale images for image processing. It takes several hours to process the X-ray films and carryout the scanning.
Fig. 3. The two-stage extrusion algorithm.
Next, the unused interior entities in each view will pass through a filtering process in which all redundant entities are removed. If all interior entities are discarded during filtering, the second-stage extrusion will be omitted. The basic-solid will be the unique solution-solid. On the other hand, if some interior entities remain after filtering, they will be swept in the second-stage extrusion to form an excess-solid. In this
Fig. 4. X-ray apparatus (the Rigaku 200EG-S3 X-ray system).
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Fig. 5. An X-ray imaging system.
3.2. Image processing Since raster images are simply a collection of pixels, distortion will result if the size of the bitmap is increased or reduced without vectorizing it. Furthermore, the raw images cannot be used directly but should be enhanced prior to solid reconstruction. One solution is to use commercial computer packages such as Adobe Photoshop [22] and CorelDRAW [23] software. Photoshop works well on the early processing
of image filtering and edge detection. In Photoshop, there are a number of operations that can enhance the images, such as orientating the images, removing unwanted areas from images, sharpening edges, extracting edges from the images, etc. Fig. 6 shows a series of image processing operations used. In CorelDRAW, the pre-processed bitmap images are converted into line drawings. The CorelTRACE module (of CorelDRAW) is used to trace the profile geometry from the raster edge pixels. The traced files are then converted into
Fig. 6. Image processing operations used in solid reconstruction: (a) orientating the image; (b) adjusting the pixel value in the image; (c) adjusting all pixel values by brightness/contrast; (d) detecting edges from the image by filter—find edges; (e) tracing the geometry by the centerline method; (f) AutoCAD geometry.
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with their associate vertices in the other views. A Cartesian coordinate system as shown in Fig. 7 is assigned to each view-contour (i.e. exterior line drawings in each view) in order to establish the point correspondence among the line drawings in third angle projection (see Fig. 8).
4. Results 4.1. Example 1 Fig. 7. The coordinate systems for all views.
Fig. 8. Three view-contours with the coordinate system assigned.
2D line drawings (i.e. .dxf format) by the DRAW module (of CorelDRAW). The 2D line drawings will then act as the input for solid reconstruction. 3.3. Solid reconstruction The two-stage extrusion program is written in the AutoLISP programming language. It is used to construct a unique 3D solid from 2D line drawings. Prior to inputting to the program, the correspondences among the six views are defined according to their geometric relationships in the object. As a result, all vertices in one view are consistent
Two examples will be used to demonstrate the proposed solid reconstruction method. Firstly, X-ray images are captured from Object-1 (a steel block: 100:00 mm 60:00 mm 60:00 mmÞ as shown in Fig. 9. The images are processed into line drawings as shown in Fig. 10 with minor human amendment since there are a few perspective distortions in the images. In the processing, three contours are extruded along their normal direction with respect to the object dimensions (i.e. length, width and height) to form three individual extrusion-solids. The three extrusion-solids are then intersected to produce a basic-solid as shown in Fig. 11. In the second stage, the non-redundant interior line drawings are swept to generate two excess-solids which are then subtracted from the basic-solid to form the final solution-solid as shown in Fig. 12. 4.2. Example 2 For the second example, X-ray equipment is used to capture the image of Object-2 (an aluminum block: 51:00 mm 24:90 mm 22:00 mm) which contains one through-hole and two blind holes of different depths, as shown in Fig. 13. The images are processed into line drawings as shown in Fig. 14. The basic-solid is simply formed by extruding the three rectangular contours. Since the interior entities remain after the filtering, they are used in the second-stage extrusion to form two cylindrical
Fig. 9. Three X-ray images of Object-1 arranged in third angle projection.
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Fig. 13. Three X-ray images of Object-2 arranged in third angle projection.
Fig. 10. Line drawings corrected with human interaction.
Fig. 14. Line drawings of Object-2. Fig. 11. The formation of a basic-solid from the extrusion of three contours: (a) the extrusion of three contours; (b) the basic-solid.
excess-solids. Finally, the basic-solid subtracts the two excess-solids to generate the 3D solution-solid, as shown in Fig. 15. Fig. 15. The solution-solid of Object-2.
5. Estimation of accuracy It is difficult to obtain exact dimensions of line drawings from whatever input methods: it will have deviations which usually result from image capturing (Ecap) and solid reconstruction (Esr) (see Fig. 16). The former deviation (Ecap) is mainly due to perspective effect caused by non-parallel projection of X-rays onto the image sensor (see Fig. 5). Further, this error is also due to image processing resulting from the maximum variation of pixel range at the edges of an
image. It is found that the maximum variation is 2 pixels (see Fig. 17) for a Kodak DC120 digital camera of resolution 1280 960. The latter deviation due to solid reconstruction can be negligible (i.e. Esr ¼ 0), since the input line drawings are corrected manually. The accuracy of the method is studied and analyzed for the worst cases in the implementation. Only the overall length, width and height of each workpiece are measured to
Fig. 12. The formation of a solution-solid: (a) the basic-solid; (b) two excess-solids; (c) the solution-solid.
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Fig. 17. An example to show the pixel variation of an image (assume that the maximum error is 2 pixels).
those for the smaller size workpiece (Object-2) are much less significant. Referring to Fig. 5, it is concluded that the perspective distortion can be minimized for a large point source-to-object distance together with a small object-tofilm distance (Table 1).
6. Discussion 6.1. Image acquisition
Fig. 16. Errors due to image capturing (Ecap) and solid reconstruction (Esr).
estimate the accuracy of the input method. The workpieces are prepared by precision machining. The actual sizes of workpieces are as follows: Object-1, 100:00 mm 60:00 mm 60:00 mm (refer to Fig. 9); Object-2, 51:00 mm 24:90 mm 22:00 mm (refer to Fig. 13). It is found that the errors due to the perspective effect for the larger size workpiece (Object-1) are significant while
One of the main problems of image capture in the implementation is the perspective distortion of images. This affects the image quality, which will in turn affect the result of solid reconstruction. Projection is required to be orthographic so that it can represent the true scale size of an object in the reconstruction. However, for the present X-ray equipment, X-rays are emitted from a point source, and thus it inherently has perspective distortion. If the distance between the point source and the object is very large, the incident radiation is nearly a parallel beam. However, due to the inverse-square law, the intensity is decreased. Therefore, the point source should be as far away as practically allowed, so that the amount of distortion is kept small. In addition, the distance between the object and the film should also be small for the same reason.
Table 1 Deviation due to the perspective effect (Ecap) Object-1
Measured length ¼ 106:74 mm 2 pixels ¼ 106:74 mm ð2=1280Þ 195:28 mm ðsince 1280 pixels is equivalent to 195:28 mmÞ ¼ 106:74 0:31 mm ¼ 106:43 mm ðminimumÞ ¼ 107:05 mm ðmaximumÞ Minimum absolute error ¼ 106:43 100:00 ¼ 6:43 mm Maximum absolute error ¼ 107:05 100:00 ¼ 7:05 mm Minimum relative error ¼ ð106:43 100:00Þ=100:00 100% ¼ 6:43% Maximum relative error ¼ ð107:05 100:00Þ=100:00 100% ¼ 7:05%
Object-2
Measured width ¼ 24:71 mm 2 pixels ¼ 24:71 0:31 mm ðuse the same pixel error as aboveÞ ¼ 24:40 mm ðminimumÞ ¼ 25:02 mm ðmaximumÞ Minimum absolute error ¼ 24:40 24:90 ¼ 0:50 mm Maximum absolute error ¼ 25:02 24:90 ¼ 0:12 mm Minimum relative error ¼ ð24:40 24:90Þ=24:90 100% ¼ 2% Maximum relative error ¼ ð25:0224:90Þ=24:90 100% ¼ 0:48%
Average errors of the two examples
Average minimum error ¼ ð6:43 þ 0:50Þ=2 ¼ 3:47 mm Average maximum error ¼ ð7:05 þ 0:12Þ=2 ¼ 3:59 mm Average error ¼ ð6:42 þ 7:05 þ 0:5 þ 0:12Þ=4 ¼ 3:525 mm
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level. The boundaries between the various gray levels thus reveal the geometric information of the object. However, an X-ray is not able to differentiate the line entity clearly if the difference between the thicknesses of two steps is not significant. The use of X-ray films has several shortcomings that can be overcome by employing an electronic image acquisition system. Nowadays, an X-ray detector can be incorporated with the X-ray image converter tube attached to a CCD camera. This technology is more accurate and efficient in image acquisition, but is much more expensive. 6.2. Cost comparison There are many different approaches to capture input data for solid reconstruction. The cost of input is a crucial factor to be considered in selection. To compare the costs of different approaches, the unit costs of relevant items are listed in Table 2. From Table 3, the lowest cost method is to apply the visible image acquisition approach (i), but the input geometric domain cannot cover hidden areas of the object. The setup time and processing time are also short. The proposed approach (ii) of using traditional X-ray imaging can offer a wider input domain, but the cost is six times higher than that for the first approach, the difference being due to the more expensive X-ray equipment. The approach (iii) of using digital X-ray imaging can provide a shorter processing time, but the cost is much higher than that of the second approach. The approach (iv) of using 3D digitizing is expensive, and it is unable to capture the internal information of an object. The outputs are point clouds which cannot be constructed explicitly by the present solid reconstruction methods. The computed tomography (CT) approach (v) is too expensive to be afforded by small- or medium-sized manufacturing industries, even though CT is able to acquire both interior and exterior information of an object precisely and very quickly. The CMM approach (iv) is also expensive. Moreover, this approach cannot be automated for one-off measurement, and the setup time and processing time are very long. Fig. 18. Operations to correct perspective distortion: (a) the original image with inclined lines and distorted circles; (b) selecting the image in horizontal and vertical reference guides; (c) correcting distortion by adjusting the corner points around the edges; (d) the corrected image.
Since perspective effect cannot be eliminated completely, minimum human interaction of the images is employed to correct any ‘‘inclined’’ parallel edges. Photoshop has been used to correct any perspective distortion of images, as shown in Fig. 18. Fortunately, X-ray imaging is unlikely to be affected by surface texture since the image is produced from radiation penetrating the material. In fact, the gray levels of a radiographic image depend on the various material thicknesses of an object. The thicker the material, the lighter is the gray
Table 2 Current unit price in the market (1999) Item
Equipment
A B C D E F G
Diffuse front-light setup 5000 Kodak DC120 digital camera 6390 Photoshop 5680 CorelDRAW 3850 AutoCAD 24960 Rigaku X-ray System with film processing installation 280000 Rich. Seifert DP210 Radioscopic X-ray System with 686500 digital Image Enhancement System VISTAPLUS II 3D digitizer 550000 CT 10000000 Coordinate Measuring Machine (CMM) 700000
H I J
Unit price (HK$)
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Table 3 Cost comparison for different data acquisition approaches Approach
Different data acquisition approaches
Investment (HK$)
Setup time and processing time
i ii iii iv v vi
Visible light image acquisition approach: A þ B þ C þ D þ E Traditional X-ray imaging approach: C þ D þ E þ F Visible light þ digital X-ray imaging approach: C þ D þ E þ G 3D digitizer approach: C þ D þ E þ H CT approach: C þ D þ E þ I CMM approach: E þ J
45880 314490 720990 584490 10034490 724960
45 min 1 day 3h 3h 1h 6h
The two-stage extrusion is also superior to shape from X in terms of accuracy. The former is a high-level processing which constructs information-complete solid model from line drawings, whilst the latter is a low-level processing which only generates an approximate shape from the image.
Acknowledgements This work was supported by a grant from The Hong Kong Polytechnic University (Project No. G-V124).
Appendix A. AutoLISP program for two-stage extrusion Fig. 19. Alternative input methods for solid reconstruction.
Other than the investment cost, the running cost and the maintenance cost for approaches (ii), (iii) and (v) are also considerable. In addition, operation safety rules [24] should be observed stringently during their operations. 6.3. Future work The input of reverse engineering is not necessarily a physical object. Fig. 19 shows two possible input methods for solid reconstruction. The input image can be captured by a sensor (a digital camera or X-ray apparatus) from a physical object, or from scanning old 2D paper drawings or their combinations.
7. Conclusions An original solid reconstruction method has been discussed. The result of solid reconstruction from multiple orthographic views is more accurate and superior to that from single-view object recognition, since the former contains more useful information. However, the input domain of the method is currently confined to polyhedral objects. In addition, 2D line drawings inevitably need to be corrected by human interaction prior to solid reconstruction due to inherent perspective distortion. Nevertheless, the X-ray radiographic images are not affected much by the environmental lighting conditions nor the surface texture of the object.
(defun 2_stage_extrusion() (input 2D line drawings from the three views of top, front, right) (first_stage_extrusion for the boundary entities to form three basic-solids) (filter out redundant interior entities) (if (non-redundant interior entities exist) (second_stage_extrusion for the non-redundant interior entities to form an excess-solid) ;then if (setq excess-solid 1) ;else if ) ;end if (subtract the excess-solid from the basic-solid to produce the solution-solid) ) (defun first_stage_extrusion() (setq i 1) (while view(i) (select 2D line drawings which belong to boundary entities) (form contour area Ai) (sweep contour area Ai along its normal vector) (solid generated is stored in Se(i) as an extrusionsolid) (setq i (þi 1)) ) ;end while (setq j 1) (while (extrusion-solid Se(j)) (intersect extrusion-solid Se(j))
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(solid generated is stored in S3v(TFR) as the basic-solid) (setq j (þj 1)) ) ) (defun second_stage_extrusion() (setq k 1) (while view(k) (select non-redundant entities) (remove non-sense entities) (form the interior region ak) (sweep interior region ak along its normal vector) (solid stored in Se(k) as the interior extrusionsolid) (setq k (þ k 1)) ) (setq l 1) (while Se(l) (intersect Se(l)) (solid stored in S3v(TFR) as the interior excesssolid) (setq l (þ l 1)) ) )
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