ofN u c l e a r
European Journal
Eur. J. Nucl. Med. 2, 129-131 (1977)
Medicine
© by Springer-Verlag 1977
A New Display Technique for Computer-Processed Digital Scans B. L e g r a s 1, J.L. M a l l e t 2, N . C h a u t, J.P. L a m b e r t 3, J. M a r t i n t a n d J. L e g r a s 3 Section d'Informatique Mbdicale (Unit6 U. 115), Facult6 de M6decine, Nancy, France Ecole de G6ologie, Nancy, France 3 D6partement de Math6matiques Appliqu6es, Facult6 des Sciences, Nancy, France
Abstract. T h i s article p r e s e n t s a n e w a p p r o a c h for p r e s e n t i n g s c i n t i g r a p h i c images. T h e t e c h n i q u e c o m b i n e s the c o n v e n t i o n a l p l o t t i n g o f c o n t o u r lines a n d t h e h i g h l i g h t i n g , b y m e a n s o f h a t c h i n g , o f the c o n c a v ities (or c o n v e x i t i e s ) o f the ' s u r f a c e ' r e p r e s e n t a t i v e o f r a d i o a c t i v e d i s t r i b u t i o n . T h e s e a r c h for the surface f e a t u r e s is a c h i e v e d g e n e r a l l y b y t h e m e t h o d o f n o r mal curvatures. An example with a phantom demonstrates t h e u t i l i t y o f this r e p r e s e n t a t i o n m e t h o d .
M Ig
X
Introduction Fig. 1. Main radii of normal curvature of surface S at point M A c c u r a t e k n o w l e d g e o f t h e ' r e l i e f ' o f the s c i n t i g r a p h 'surface' which characterizes the radioactive distribut i o n o f a n i s o t o p e is i m p o r t a n t , in p a r t i c u l a r its features, w h i c h m a y c o r r e s p o n d to k n o w n a n a t o m i c s t r u c t u r e s or to u p t a k e irregularities. S o m e a u t h o r s h a v e i n v e s t i g a t e d t h e a u t o m a t i c h i g h l i g h t i n g o f concavities b y c o m p u t e r ( G r a s s m a n e t a l . , 1970; Neill et al., 1971) b u t these i n v e s t i g a t i o n s h a v e b e e n c a r r i e d o u t o n profiles o f the s u r f a c e a n d c o n s i s t i n c o m p a r i n g the m e a s u r e d v a l u e s w i t h t h e a v e r a g e values. T h e s e t e c h n i q u e s a r e useful, b u t it a p p e a r s m o r e i n t e r e s t i n g a n d m o r e logical to e x a m i n e s u r f a c e singularities i n a n o v e r a l l m a n n e r , a n d the a u t h o r s were led to e m p l o y the m e t h o d o f n o r m a l curves, a m e t h o d w h i c h does n o t d e p e n d o n d i r e c t i o n s b u t o n l y o n t h e i n t r i n s i c p r o p e r t i e s o f the surface.
Method A classic proof in differential geometry shows that among all planes passing through a point M of an area defined by J(x, y) and containFor offprints contact: Dr. B. Legras, Section d'Informatique M6di-
cale, Facnltb de M6decine B.P. 1080, F-54019 Nancy-C6dex, France
(Rt = MC1, Ra =
MC2)
ing the normal N at this point, two planes P1 and P2 exist, which are perpendicular to each other and such that the corresponding radii of curvature R1 and R2 are the shortest and longest possible (Fig. 1). R1 and R2 are the principal (normal) radii of curvature and C1 = 1/Rx and C2 = 1/R2 are the principal normal curvatures. The determination of R~ and R2 requires the calculation of the first and second partial derivatives of f. In order to estimate these derivatives at each point of the scintiscan, the program employed ~ carries out a local interpolation by a polynomial of determined degree at x and at y on a selected window 2. The representations adopted employ a curve plotter 3 and associate the plotting of isocontonrs with the revelation of concavities (or convexities) by normal curvatures. The program hatches the zones in which both curvatures C1 and C; have the same selected sign (negative in the study of concavities). It determines their respective means C~1 and CM2 and at The program is written in FORTRAN IV and its size is about 2 K octets 2 The window is centered on the point considered whenever possible, or not centered in other cases (edges of area studied). Local interpolation is achieved by Lagrange's method. The best results are provided by a 4th degree polynomial at x and at y and a 25-points window 3 Curve plotter Calcomp used off-line
130
B. Legras et al. : A New Display Technique for Computer-Processed Digital Scans
areas where ICxl>lC~ll and I C~l>[CM21 simultaneously, it overprints hatching perpendicular to the previous hatching. Hence the more pronounced and consequently more significant anomalies are easily localized. Many other procedures are feasible. One involves the use, at each point, of the maximum curvature only. Curvatures can also be more highly quantified by using a greater number of hatchings.
Results
In order to illustrate these representation techniques, the authors have chosen the scintiscan of a liver phantom, more accurately described in another article (Legras et al., 1972). It is carrying two lead discs which simulate two pathologic cold lesions. The upper one is visible on the black white scan unlike the lower cold lesion. The value matrix is 64 x 64 and the maximum measured value is equal to 240. The raw values obtained were smoothed by an original method (Lambert, 1975). This smoothing is carried out simultaneously on all the values by a poly-
Fig. 2. Contour lines of smoothed digital scan of phantom liver (equidistant levels of I0% of the maximum smoothed value)
Fig. 4. Representation of concavities of smoothed di :ital scan of phantom liver by the method of normal curvatures in association with contour lines. Two types of hatching are used, depending on the value of the two radii of curvature
nomial at x and at y by the method of the least squares. Two statistical tests applied to raw and smoothed values provide information on smoothing quality (Legras, 1972) and help to choose the polynomial degree. In our example, we have used a 10th degree polynomial and we shall allow as true that the smoothed surface is characteristic of the radioactive distribution. Only the concavities are considered here. Figure 2 shows the classic representation by isocontours. They clearly reveal the upper cold zone but merely suggest the lower one. The isometric representation which has been used in nuclear medicine since 1964 (Duggan et al.) shows the two anomalies more clearly (Fig. 3). The representation ~associating isocontours and concavities (Fig. 4) enables perfect display of the two cold lesions. Furthermore, it objectifies the small hollows which are very difficult to evaluate from isocontours.
letric representation of smothed digital scan of phantom orientation as Fig. 2)
B. Legras et al. : A New Display Technique for Computer-Processed Digital Scans
131
Note that the various representations are not effected below a basic level defined by a certain percentage of the maximum value (30% in the present example).
ing the graphic representation to obtain more advanced quantification. This representation, which is the result of extensive tests, appears to be easier to interpret.
Discussion and Conclusions
References
The classic representation of computer-processed scintiscans uses the isocontour method. If the grid is very dense, however, the document is difficult to read, and if the grid is loose, the curves may tend to ignore interesting zones (which is the case with the lower hypofixing zone not displayed in Fig. 2). The isometric representation is more expressive but has two d r a w b a c k s - a n o m a l i e s may be masked, depending on the sight angle, and it is difficult to establish precisely the magnitude and location of the anomalies. The new type of representation described in this article furnishes in a single document the isocontours and complementary information on the relief of the surface. The isocontours give a general idea of the surface, and the shaded zones immediately locate the cold zones. In this initial study, a sufficient degree of quantification of the concavities was achieved to satisfy current needs. There is no problem in modify-
Duggan, M.H., Brice, J., Jones, E., Mallard, J.R., Myers, M.I.: Scanning techniques for b r a i n - t u m o u r localization. Med. Radioisot. Scanning (IAEA Vienne) II, 121-145 (1964) Grassman, E.D., Horgan, J.D., Maeder, C.: Quantitative analysis of liver scan data as on aid diagnosis. Radiology 95, 517-523 (1970) Lambert, J.P. : Etude par simulation des lissages polynomiaux des scintigraphies num+riques avec contr61e statistique. Th+se 100 p. (1975) Legras, B. : Analyse de diff6rentes repr6sentations des scintigraphies num6riques traitees par ordinateur. M6moire D.E.R.B.H., 70 p. (1975) Legras, B., Potdevin, M., Martin, J.: Statistical verification of the smoothing of low scanning values. A study by simulation and with a phantom. J. nucl. Meal. 13, 528 (1972) Mallet, J.L. : Pr6sentation d'un ensemble de mSthodes et techniques de la cartographie numSrique. Sciences de la Terre 4, No. 4, 212 p. (1974) Neill, G.D.S., Hutchinson, F.: Computer detection and display of focal lesions on scintiscans. Brit. J. Radiol. 962-967 (1971)
Received October 11, 1976
European Journal
Eur. J. Nucl. Med. 2, 129-131 (1977)
Medicine
© by Springer-Verlag 1977
A New Display Technique for Computer-Processed Digital Scans B. L e g r a s 1, J.L. M a l l e t 2, N . C h a u t, J.P. L a m b e r t 3, J. M a r t i n t a n d J. L e g r a s 3 Section d'Informatique Mbdicale (Unit6 U. 115), Facult6 de M6decine, Nancy, France Ecole de G6ologie, Nancy, France 3 D6partement de Math6matiques Appliqu6es, Facult6 des Sciences, Nancy, France
Abstract. T h i s article p r e s e n t s a n e w a p p r o a c h for p r e s e n t i n g s c i n t i g r a p h i c images. T h e t e c h n i q u e c o m b i n e s the c o n v e n t i o n a l p l o t t i n g o f c o n t o u r lines a n d t h e h i g h l i g h t i n g , b y m e a n s o f h a t c h i n g , o f the c o n c a v ities (or c o n v e x i t i e s ) o f the ' s u r f a c e ' r e p r e s e n t a t i v e o f r a d i o a c t i v e d i s t r i b u t i o n . T h e s e a r c h for the surface f e a t u r e s is a c h i e v e d g e n e r a l l y b y t h e m e t h o d o f n o r mal curvatures. An example with a phantom demonstrates t h e u t i l i t y o f this r e p r e s e n t a t i o n m e t h o d .
M Ig
X
Introduction Fig. 1. Main radii of normal curvature of surface S at point M A c c u r a t e k n o w l e d g e o f t h e ' r e l i e f ' o f the s c i n t i g r a p h 'surface' which characterizes the radioactive distribut i o n o f a n i s o t o p e is i m p o r t a n t , in p a r t i c u l a r its features, w h i c h m a y c o r r e s p o n d to k n o w n a n a t o m i c s t r u c t u r e s or to u p t a k e irregularities. S o m e a u t h o r s h a v e i n v e s t i g a t e d t h e a u t o m a t i c h i g h l i g h t i n g o f concavities b y c o m p u t e r ( G r a s s m a n e t a l . , 1970; Neill et al., 1971) b u t these i n v e s t i g a t i o n s h a v e b e e n c a r r i e d o u t o n profiles o f the s u r f a c e a n d c o n s i s t i n c o m p a r i n g the m e a s u r e d v a l u e s w i t h t h e a v e r a g e values. T h e s e t e c h n i q u e s a r e useful, b u t it a p p e a r s m o r e i n t e r e s t i n g a n d m o r e logical to e x a m i n e s u r f a c e singularities i n a n o v e r a l l m a n n e r , a n d the a u t h o r s were led to e m p l o y the m e t h o d o f n o r m a l curves, a m e t h o d w h i c h does n o t d e p e n d o n d i r e c t i o n s b u t o n l y o n t h e i n t r i n s i c p r o p e r t i e s o f the surface.
Method A classic proof in differential geometry shows that among all planes passing through a point M of an area defined by J(x, y) and containFor offprints contact: Dr. B. Legras, Section d'Informatique M6di-
cale, Facnltb de M6decine B.P. 1080, F-54019 Nancy-C6dex, France
(Rt = MC1, Ra =
MC2)
ing the normal N at this point, two planes P1 and P2 exist, which are perpendicular to each other and such that the corresponding radii of curvature R1 and R2 are the shortest and longest possible (Fig. 1). R1 and R2 are the principal (normal) radii of curvature and C1 = 1/Rx and C2 = 1/R2 are the principal normal curvatures. The determination of R~ and R2 requires the calculation of the first and second partial derivatives of f. In order to estimate these derivatives at each point of the scintiscan, the program employed ~ carries out a local interpolation by a polynomial of determined degree at x and at y on a selected window 2. The representations adopted employ a curve plotter 3 and associate the plotting of isocontonrs with the revelation of concavities (or convexities) by normal curvatures. The program hatches the zones in which both curvatures C1 and C; have the same selected sign (negative in the study of concavities). It determines their respective means C~1 and CM2 and at The program is written in FORTRAN IV and its size is about 2 K octets 2 The window is centered on the point considered whenever possible, or not centered in other cases (edges of area studied). Local interpolation is achieved by Lagrange's method. The best results are provided by a 4th degree polynomial at x and at y and a 25-points window 3 Curve plotter Calcomp used off-line
130
B. Legras et al. : A New Display Technique for Computer-Processed Digital Scans
areas where ICxl>lC~ll and I C~l>[CM21 simultaneously, it overprints hatching perpendicular to the previous hatching. Hence the more pronounced and consequently more significant anomalies are easily localized. Many other procedures are feasible. One involves the use, at each point, of the maximum curvature only. Curvatures can also be more highly quantified by using a greater number of hatchings.
Results
In order to illustrate these representation techniques, the authors have chosen the scintiscan of a liver phantom, more accurately described in another article (Legras et al., 1972). It is carrying two lead discs which simulate two pathologic cold lesions. The upper one is visible on the black white scan unlike the lower cold lesion. The value matrix is 64 x 64 and the maximum measured value is equal to 240. The raw values obtained were smoothed by an original method (Lambert, 1975). This smoothing is carried out simultaneously on all the values by a poly-
Fig. 2. Contour lines of smoothed digital scan of phantom liver (equidistant levels of I0% of the maximum smoothed value)
Fig. 4. Representation of concavities of smoothed di :ital scan of phantom liver by the method of normal curvatures in association with contour lines. Two types of hatching are used, depending on the value of the two radii of curvature
nomial at x and at y by the method of the least squares. Two statistical tests applied to raw and smoothed values provide information on smoothing quality (Legras, 1972) and help to choose the polynomial degree. In our example, we have used a 10th degree polynomial and we shall allow as true that the smoothed surface is characteristic of the radioactive distribution. Only the concavities are considered here. Figure 2 shows the classic representation by isocontours. They clearly reveal the upper cold zone but merely suggest the lower one. The isometric representation which has been used in nuclear medicine since 1964 (Duggan et al.) shows the two anomalies more clearly (Fig. 3). The representation ~associating isocontours and concavities (Fig. 4) enables perfect display of the two cold lesions. Furthermore, it objectifies the small hollows which are very difficult to evaluate from isocontours.
letric representation of smothed digital scan of phantom orientation as Fig. 2)
B. Legras et al. : A New Display Technique for Computer-Processed Digital Scans
131
Note that the various representations are not effected below a basic level defined by a certain percentage of the maximum value (30% in the present example).
ing the graphic representation to obtain more advanced quantification. This representation, which is the result of extensive tests, appears to be easier to interpret.
Discussion and Conclusions
References
The classic representation of computer-processed scintiscans uses the isocontour method. If the grid is very dense, however, the document is difficult to read, and if the grid is loose, the curves may tend to ignore interesting zones (which is the case with the lower hypofixing zone not displayed in Fig. 2). The isometric representation is more expressive but has two d r a w b a c k s - a n o m a l i e s may be masked, depending on the sight angle, and it is difficult to establish precisely the magnitude and location of the anomalies. The new type of representation described in this article furnishes in a single document the isocontours and complementary information on the relief of the surface. The isocontours give a general idea of the surface, and the shaded zones immediately locate the cold zones. In this initial study, a sufficient degree of quantification of the concavities was achieved to satisfy current needs. There is no problem in modify-
Duggan, M.H., Brice, J., Jones, E., Mallard, J.R., Myers, M.I.: Scanning techniques for b r a i n - t u m o u r localization. Med. Radioisot. Scanning (IAEA Vienne) II, 121-145 (1964) Grassman, E.D., Horgan, J.D., Maeder, C.: Quantitative analysis of liver scan data as on aid diagnosis. Radiology 95, 517-523 (1970) Lambert, J.P. : Etude par simulation des lissages polynomiaux des scintigraphies num+riques avec contr61e statistique. Th+se 100 p. (1975) Legras, B. : Analyse de diff6rentes repr6sentations des scintigraphies num6riques traitees par ordinateur. M6moire D.E.R.B.H., 70 p. (1975) Legras, B., Potdevin, M., Martin, J.: Statistical verification of the smoothing of low scanning values. A study by simulation and with a phantom. J. nucl. Meal. 13, 528 (1972) Mallet, J.L. : Pr6sentation d'un ensemble de mSthodes et techniques de la cartographie numSrique. Sciences de la Terre 4, No. 4, 212 p. (1974) Neill, G.D.S., Hutchinson, F.: Computer detection and display of focal lesions on scintiscans. Brit. J. Radiol. 962-967 (1971)
Received October 11, 1976
