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Non-stationary metz-filtering
172
Abstracts
Non-Stationary Metz-Filtering, by GUSTAFS- The average direction (0) can also be determined by the second order moments of the variable shape SONT. R. and PIZER S. M. Radiofysiska Cenfilter, i.e. trallaboratoriet, Lasarettet, S-221 85 LUND, Sweden and Dept. of Computer Science, Unis +s,,+SSQ Elong.’ = *’ versity of North Carolina, Chapel Hill, NC s,, + S,, - SSQ 275 14, U.S.A. S,, - S,, f SSQ tan(e)= 2s p IntrodIlcfiorJ XY where A TECHNIQUE is presented which combines the good smoothing and gradient-preserving properties of the non-stationary variable shape smoothing reported at the second conference in this series,(‘*‘) and the good enhancement properties of the Metzfilter.‘3-5’ The variable shape smoothing is, by the very nature, not particularly good for detection of small lesions, since it is a smoothing filter, and thus suppresses the components of high spatial frequencies. This disadvantage can be compensated by combining the smoothing with refocussing filtering. proeeaping tedmique The fundamental idea is to increase the signal-tonoise ratio with variable shape smoothing and follow this by a refocussing Me&filtering applied only in directions perpendicular to that of the previous smoothing, since there is little meaning in smoothing and refocussing in the same direction. Variable shape smoothing The filtering is performed in two stages, the first stage of which is the variable shape smoothing. This phase can be thought of as a position dependant smoothing along the contours in the image. Furthermore not only does the shape of the filter adjust itself to the surroundings, but also the size of the filter varies in such a way that the filter-area is inversely proportional to the local count density. The advantage with this type of smoothing is a considerable reduction of the noise while preserving the gradients much more satisfactorily than conventional smoothing. The edge effects are also minimal. Filter elongation and diredon In order to perform the second step of the filtering procedure, the elongation and the average direction of the set of filter-points must be computed for each point in the image. This is done in the following manner: The characteristic equation for the second order moments is solved with respect to the eigen-value A. The elongation is formed by the two roots A1 and hZ: Elong.’ = 2. 2
SSQ = d( S,, - S,,)’ + 4S,, and s, =8(x,‘-%) S,, = Z(Y? - Y) s,, = Z(XiYi- fy). The image must first be filtered entirely with variable shape smoothing and thereafter with directional Me&filtering. This implies that both direction and elongation must be stored for each pictureelement. The average direction for the variable shape filter (6) gives the direction in which enhancement is not to be done. One of four different directions is used for the l-dimensional filter. According to the value of 0, the appropriate direction is selected for the corresponding angular interval. Should the elongation be less than 1.1 the direction is set to zero, flagging an isotropic region (an elongation of 1.0 indicates a circular filter). 1 2
3
*
4
This requires two bits of information to be stored for each element. The elongation is used to control the refocussing effect of the Me&titer. The actual value of the elongation is not stored, but it is divided into three groups labelled 1, 2 and 3. This also requires 2 bits, and these 4 bits can either be stored as the most significant bits in the picture matrix itself, which does not require more memory space, or it can be stored in a packed array. 1-dtmens&nal M&z-tgter The first step has increased the signal-to-noise ratio considerably without deteriorating the gradients in the picture. Furthermore, the statistical error is approximately constant. This is an advantageous situation for applying a refocussing filter. Such a filter should preferably not have any effect in directions in which smoothing has already been
Abstracts
173
scintigraphic data, e.g. grey tone-, isocontour presentation, contrast enhancement, filtering, smoothing etc. But unfortunately development of methods to use these techniques most efficiently in the daily routine of clinical environment has been neglected. For example the set of programs, which exists in a typical scintigraphic system and which is assigned to standard keyboard or lightbutton functions, is usually hard to extend due to the fact that these systems are written to a very large extent in assemElong. Label order(N) bler language and only to a small amount in Fortran or in other high or medim level languages. s 1.0-2.0 1 The values are Systems of this kind have been implemented in 8 2.0-3.0 2 15 arbitrarily chosen. > 3.0 3 several places. (I) Experience of the authors with the system ISAAC”’ shows-although it has been used successfully for about 3 years-that the rigid The FWHM of the associated point-spread function scheme of executing analysis programs does not is kept constant. The filtering with the linear Metzquite reflect the procedure in which a physician filter is performed as a 2-pass filtering, where the finds a diagnosis. This procedure is usually an iterasecond pass is used for filtering isotropic areas with tive process,(3) i.e. the finding results from many a perpendicular linear filter. Thus, a 2-pass lsingle analysis steps, each depending of the foregodimensional filtering is performed for all elements ing step as well as on the respective scintigraphic with a direction-label equal to zero, i.e. in isotropic data. regions. In order to overcome the gap between practical requirements and the existing more or less rigid References system, it was decided to develop a dialog- lan1. GUST-SON T. and TODD-POKROPEK A. Filters guage,@+)with the aim to combine both, application with variable shape in radioisotope image proof standard analysis techniques and the possibility cessing. To be published. to develop new applications in a fast and easy 2. GUSTAF~SON T. and TODD-POKROPEK A. Demanner in dialog with the computer. Easy developsign and application of filters with variable ment of new applications implies in particular shape. 2nd European Meeting Data Handling definition of data types sgycially suited for procesand Image Processing in Scintigraphy, Hannover (i.e. images, regions of sing of scintigraphic data (1971) In press. the corresponding combined with interest) 3. METZ C. E. A mathematical investigation of operators. radioisotope scan image processing. Doctoral Keeping in mind that future users of the system, thesis, University of Pennsylvania, 1969. namely physicians, assistents, etc. have little or no 4. GUST-SON T. MILLER T. R. and NAVERSTEN computer experience, some conditions for the deY. 2nd European Meeting Data Handling and sign of the language must be met: (1) easy to learn Hannover Image Processing in Scintigraphy and to use, (2) wide range of applications, (3) short (1971) In press. reaction times to commands, and last not least, (4) 5. MUELLERT. R., GUST-SON T., NAVERSX%NY. high reliability in operation. and CEDERQUIST E. Experiences of computer Mostly the demand for easy learning and using a evaluation of thyroid. scans in clinical routine. language is contradictory to having a wide range of Proc. Symp. Medical Radioisotope Scintigraphy, applications and a compromise between complexity 1972, Vienna. of language structure and the ease of use should be found. Therefore two levels of operations are disA Dialog Language for interactive Processing tinguished: (1) exclusive use of pre-defined operations, which may be selected from “menus” by of Scintfgrapbic Data, by H~HNE K. H. and light-pen. No knowledge at all of the language is PFEIFFER G. Deutsches Elektronen-Synrequired. (2) explicit use of the language to formuchrotron DESY, 2 Hamburg 52, Notkestieg 1, late new problems or to create new sets of menus. Germany. In the design of a dialog language it is useful to DURING these last years powerful tools have been refer to existing conversational languages as moddeveloped for presentation as well as ‘for analysis of els, although they have primarily been designed for performed. Therefore a l-dimensional Me&filter is applied in directions parallel -to the gradients in the image. The enhancement filter can also be made non-stationary in another sense, namely by making its effect be proportional to the magnitude of the local gradient. This is done by means of adjusting the order of the iterative Metz-!ilter according to the elongation group label, i.e. the more elongated the filter, the higher the value of N, e.g.
Abstracts
Non-Stationary Metz-Filtering, by GUSTAFS- The average direction (0) can also be determined by the second order moments of the variable shape SONT. R. and PIZER S. M. Radiofysiska Cenfilter, i.e. trallaboratoriet, Lasarettet, S-221 85 LUND, Sweden and Dept. of Computer Science, Unis +s,,+SSQ Elong.’ = *’ versity of North Carolina, Chapel Hill, NC s,, + S,, - SSQ 275 14, U.S.A. S,, - S,, f SSQ tan(e)= 2s p IntrodIlcfiorJ XY where A TECHNIQUE is presented which combines the good smoothing and gradient-preserving properties of the non-stationary variable shape smoothing reported at the second conference in this series,(‘*‘) and the good enhancement properties of the Metzfilter.‘3-5’ The variable shape smoothing is, by the very nature, not particularly good for detection of small lesions, since it is a smoothing filter, and thus suppresses the components of high spatial frequencies. This disadvantage can be compensated by combining the smoothing with refocussing filtering. proeeaping tedmique The fundamental idea is to increase the signal-tonoise ratio with variable shape smoothing and follow this by a refocussing Me&filtering applied only in directions perpendicular to that of the previous smoothing, since there is little meaning in smoothing and refocussing in the same direction. Variable shape smoothing The filtering is performed in two stages, the first stage of which is the variable shape smoothing. This phase can be thought of as a position dependant smoothing along the contours in the image. Furthermore not only does the shape of the filter adjust itself to the surroundings, but also the size of the filter varies in such a way that the filter-area is inversely proportional to the local count density. The advantage with this type of smoothing is a considerable reduction of the noise while preserving the gradients much more satisfactorily than conventional smoothing. The edge effects are also minimal. Filter elongation and diredon In order to perform the second step of the filtering procedure, the elongation and the average direction of the set of filter-points must be computed for each point in the image. This is done in the following manner: The characteristic equation for the second order moments is solved with respect to the eigen-value A. The elongation is formed by the two roots A1 and hZ: Elong.’ = 2. 2
SSQ = d( S,, - S,,)’ + 4S,, and s, =8(x,‘-%) S,, = Z(Y? - Y) s,, = Z(XiYi- fy). The image must first be filtered entirely with variable shape smoothing and thereafter with directional Me&filtering. This implies that both direction and elongation must be stored for each pictureelement. The average direction for the variable shape filter (6) gives the direction in which enhancement is not to be done. One of four different directions is used for the l-dimensional filter. According to the value of 0, the appropriate direction is selected for the corresponding angular interval. Should the elongation be less than 1.1 the direction is set to zero, flagging an isotropic region (an elongation of 1.0 indicates a circular filter). 1 2
3
*
4
This requires two bits of information to be stored for each element. The elongation is used to control the refocussing effect of the Me&titer. The actual value of the elongation is not stored, but it is divided into three groups labelled 1, 2 and 3. This also requires 2 bits, and these 4 bits can either be stored as the most significant bits in the picture matrix itself, which does not require more memory space, or it can be stored in a packed array. 1-dtmens&nal M&z-tgter The first step has increased the signal-to-noise ratio considerably without deteriorating the gradients in the picture. Furthermore, the statistical error is approximately constant. This is an advantageous situation for applying a refocussing filter. Such a filter should preferably not have any effect in directions in which smoothing has already been
Abstracts
173
scintigraphic data, e.g. grey tone-, isocontour presentation, contrast enhancement, filtering, smoothing etc. But unfortunately development of methods to use these techniques most efficiently in the daily routine of clinical environment has been neglected. For example the set of programs, which exists in a typical scintigraphic system and which is assigned to standard keyboard or lightbutton functions, is usually hard to extend due to the fact that these systems are written to a very large extent in assemElong. Label order(N) bler language and only to a small amount in Fortran or in other high or medim level languages. s 1.0-2.0 1 The values are Systems of this kind have been implemented in 8 2.0-3.0 2 15 arbitrarily chosen. > 3.0 3 several places. (I) Experience of the authors with the system ISAAC”’ shows-although it has been used successfully for about 3 years-that the rigid The FWHM of the associated point-spread function scheme of executing analysis programs does not is kept constant. The filtering with the linear Metzquite reflect the procedure in which a physician filter is performed as a 2-pass filtering, where the finds a diagnosis. This procedure is usually an iterasecond pass is used for filtering isotropic areas with tive process,(3) i.e. the finding results from many a perpendicular linear filter. Thus, a 2-pass lsingle analysis steps, each depending of the foregodimensional filtering is performed for all elements ing step as well as on the respective scintigraphic with a direction-label equal to zero, i.e. in isotropic data. regions. In order to overcome the gap between practical requirements and the existing more or less rigid References system, it was decided to develop a dialog- lan1. GUST-SON T. and TODD-POKROPEK A. Filters guage,@+)with the aim to combine both, application with variable shape in radioisotope image proof standard analysis techniques and the possibility cessing. To be published. to develop new applications in a fast and easy 2. GUSTAF~SON T. and TODD-POKROPEK A. Demanner in dialog with the computer. Easy developsign and application of filters with variable ment of new applications implies in particular shape. 2nd European Meeting Data Handling definition of data types sgycially suited for procesand Image Processing in Scintigraphy, Hannover (i.e. images, regions of sing of scintigraphic data (1971) In press. the corresponding combined with interest) 3. METZ C. E. A mathematical investigation of operators. radioisotope scan image processing. Doctoral Keeping in mind that future users of the system, thesis, University of Pennsylvania, 1969. namely physicians, assistents, etc. have little or no 4. GUST-SON T. MILLER T. R. and NAVERSTEN computer experience, some conditions for the deY. 2nd European Meeting Data Handling and sign of the language must be met: (1) easy to learn Hannover Image Processing in Scintigraphy and to use, (2) wide range of applications, (3) short (1971) In press. reaction times to commands, and last not least, (4) 5. MUELLERT. R., GUST-SON T., NAVERSX%NY. high reliability in operation. and CEDERQUIST E. Experiences of computer Mostly the demand for easy learning and using a evaluation of thyroid. scans in clinical routine. language is contradictory to having a wide range of Proc. Symp. Medical Radioisotope Scintigraphy, applications and a compromise between complexity 1972, Vienna. of language structure and the ease of use should be found. Therefore two levels of operations are disA Dialog Language for interactive Processing tinguished: (1) exclusive use of pre-defined operations, which may be selected from “menus” by of Scintfgrapbic Data, by H~HNE K. H. and light-pen. No knowledge at all of the language is PFEIFFER G. Deutsches Elektronen-Synrequired. (2) explicit use of the language to formuchrotron DESY, 2 Hamburg 52, Notkestieg 1, late new problems or to create new sets of menus. Germany. In the design of a dialog language it is useful to DURING these last years powerful tools have been refer to existing conversational languages as moddeveloped for presentation as well as ‘for analysis of els, although they have primarily been designed for performed. Therefore a l-dimensional Me&filter is applied in directions parallel -to the gradients in the image. The enhancement filter can also be made non-stationary in another sense, namely by making its effect be proportional to the magnitude of the local gradient. This is done by means of adjusting the order of the iterative Metz-!ilter according to the elongation group label, i.e. the more elongated the filter, the higher the value of N, e.g.