Method of determining (a) symmetry line(s) in a radiation image

• US 6,263,097 B1
• Filed: 06/24/1998
• Issued: 07/17/2001
• Est. Priority Date: 07/04/1997
• Status: Expired due to Term

• Current Assignee: AGFA Healthcare NV (Agfa-Gevaert N.V.)
• Original Assignee: Agfa-Gevaert N.V.
• Inventors: Dewaele, Piet
• Primary Examiner(s): Mancuso, Joseph
• Assistant Examiner(s): TABATABAI, ABOLFAZL
• Application Number:
  US09/103,991
• Time in Patent Office: 1,119 Days
• Field of Search: 382/132, 382/174, 382/288, 382/289, 382/203, 382/217, 345/441, 345/440, 356/336, 362/347, 250/334
• US Class Current: 382/132
• CPC Class Codes: G06T 2207/10116 X-ray image
• CPC Class Codes: G06T 2207/30004 Biomedical image processing
• CPC Class Codes: G06T 7/68 of symmetry

Abstract

Method of determining (a) symmetry line(s) in a radiation image.

A method of determining (a) symmetry line(s) in horizontal (vertical) direction in an image that is represented by a matrix of digital pixel values by (i) calculating a symmetry point for each column (row) of the image, and (ii) interconnecting calculated symmetry points.

Claims

1. Method of determining a symmetry line in at least one of a horizontal direction and a vertical direction in a radiation image that is represented by a matrix of digital pixel values, comprising the steps of:

(i) calculating, in case of horizontal directions a symmetry point for each column of the image, and, in case of vertical direction, a symmetry point for each row of said image; and

(ii) interconnecting calculated symmetry points,

wherein a symmetry point for column j or row j, respectively, is obtained by;

(1) calculating for column j or row j, and for each pixel c at position i in column j or row j, symmetrical difference sum values S according to the formula;

$S<br><br>\left(i=c,j\right)=\underset{k=1}{\overset{m<br><br>\left(i\right)}{\sum <br><br>}}<br><br>[g<br><br>\left(c+k,j\right)-{\left(g<br><br>\left(c-k,j\right)\right]}^2,$

 

where c=T, . . . , M−

T−

1, g(i,j) is a gray value at position (i,j), T is an offset parameter, M is a number of rows or columns, respectively in the matrix, and m(i) equals to min (i, M−

i−

1),

(2) normalizing S to obtain {overscore (S)}, and

(3) determining a minimal value {overscore (S)}_min of the values {overscore (S)} obtained for each pixel c, and denoting a value c for which {overscore (S)} is equal to {overscore (S)}_min as the symmetry point of column j or row j, respectively.

2. Method according to claim 1 wherein $\stackrel{\_}{S}$

(c,j)=S

(c,j)m

(i)

 



c=T,…



 

,M-T-1.

3. Method according to claim 1 wherein $\stackrel{\_}{S}$

(c,j)=S

(c,j)gu

(c,j)·

(m

(i))v

 

$c=T,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>},M-T-1<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{wherein}<br><br>\text{\hspace{1em}<br><br>}<br><br>u,v\ge <br><br>1.$

4. Method according to claim 1 wherein symmetry points are interconnected to obtain a symmetry line by computing the least squares fitting on data tuples (j,C_j(j)) and an associated measurement error value (1−

R(j)), wherein R(j) is a reliability measure for each of the symmetry points.

5. Method according to claim 1 wherein a horizontal symmetry index (SI_h) is calculated as ${\mathrm{SI}}_h=\frac{1}{N}$

∑

j=0N-1

Sh

(j),

and a vertical symmetry index (SI_v) is calculated as ${\mathrm{SI}}_v=\frac{1}{M}<br><br>\underset{j=0}{\overset{M-1}{\sum <br><br>}}<br><br>S_v<br><br>\left(i\right),$

wherein a main orientation index (SI) of the image is determined as

6. Method according to claim 1 wherein an orientation angle of an image is determined as an angle between a horizontal or vertical symmetry line respectively and a horizontal or vertical coordinate axis.

7. Method of determining a symmetry line in at least one of a horizontal direction and a vertical direction in a radiation image that is represented by a matrix of digital pixel values, comprising the steps of:

(i) calculating, in case of horizontal direction, a symmetry point for each column of the image, and, in case of vertical direction, a symmetry point for each row of the image;

(ii) interconnecting calculated symmetry points; and

(iii) computing a reliability measure R(c, j) associated with a calculated symmetry point c for column j or row j, respectively, according to;

$R<br><br>\left(c,j\right)=1-\frac{1}{\sqrt{{\mathrm{\sigma <br><br>}}^2<br><br>\left(c,j\right)+1}},<br><br>\mathrm{where}$$\begin{array}{c}{\mathrm{\sigma <br><br>}}^2<br><br>\left(c,j\right)=\text{\hspace{1em}<br><br>}<br><br>\frac{1}{m}<br><br>(\underset{k=1}{\overset{m}{\sum <br><br>}}<br><br>{\left[g<br><br>\left(c-k,j\right)-g<br><br>\left(c,j\right)\right]}^2+\\ \text{\hspace{1em}<br><br>}<br><br>\underset{k=1}{\overset{m}{\sum <br><br>}}<br><br>{\left[g<br><br>\left(c+k,j\right)-g<br><br>\left(c,j\right)\right]}^2).\end{array}$

8. Method according to claim 7 wherein a horizontal symmetry index (SI_h) is calculated as ${\mathrm{SI}}_h=\frac{1}{N}$

∑

j=0N-1

Sh

(j),

and a vertical symmetry index (SI_v) is calculated as ${\mathrm{SI}}_v=\frac{1}{M}<br><br>\underset{j=0}{\overset{M-1}{\sum <br><br>}}<br><br>S_v<br><br>\left(i\right),$

wherein a main orientation index SI of the image is determined as

9. Method according to claim 7 wherein an orientation angle of the image is determined as an angle between a horizontal coordinate axis and a vertical coordinate axis.

10. Method of providing a radiation image in a position in which a horizontal or vertical symmetry line respectively in said image is parallel to a horizontal or vertical coordinate axis comprising the steps of

(i) determining a horizontal or vertical symmetry line in said image,

(ii) determining an orientation angle α

by which said image is tilted relative to a horizontal or vertical coordinate axis respectively,

(iii) rotating said image by an angle −

α

.

11. Method according to claim 10 wherein the respective symmetry line is calculated by:

(i) calculating, in case of horizontal direction, a symmetry point for each column of the image, and, in case of vertical direction, a symmetry point for each row of said image; and

(ii) interconnecting calculated symmetry points,

wherein a symmetry point for column j or row j, respectively, is obtained by;

(1) calculating for column j or row j, and for each pixel c at position i in column j or row j, symmetrical difference sum values S according to the formula;

$S<br><br>\left(i=c,j\right)=\underset{k=1}{\overset{m<br><br>\left(i\right)}{\sum <br><br>}}<br><br>[g<br><br>\left(c+k,j\right)-{\left(g<br><br>\left(c-k,j\right)\right]}^2,$

 

where c=T, . . . , M−

T−

1, g(i, j) is a gray value at position (i, j), T is an offset parameter, M is a number of rows or columns, respectively in the matrix, and m(i) equals to min (i, M−

i−

1),

(2) normalizing S to obtain {overscore (S)}, and

(3) determining a minimal value {overscore (S)}_min of the values {overscore (S)} obtained for each pixel c, and denoting a value c for which {overscore (S)} is equal to {overscore (S)}_min as the symmetry point of column j or row j, respectively.

12. Method according to claim 10, wherein the respective symmetry line is determined by:

(i) calculating, in case of horizontal direction, a symmetry point for each column of the image, and, in case of vertical direction, a symmetry point for each row of the image;

(ii) computing a reliability measure R(c, j) associated with a calculated symmetry point c for column j or row j, respectively, according to;

$R<br><br>\left(c,j\right)=1-\frac{1}{\sqrt{{\mathrm{\sigma <br><br>}}^2<br><br>\left(c,j\right)+1}},<br><br>\mathrm{where}$$\begin{array}{c}{\mathrm{\sigma <br><br>}}^2<br><br>\left(c,j\right)=\text{\hspace{1em}<br><br>}<br><br>\frac{1}{m}<br><br>(\underset{k=1}{\overset{m}{\sum <br><br>}}<br><br>{\left[g<br><br>\left(c-k,j\right)-g<br><br>\left(c,j\right)\right]}^2+\\ \text{\hspace{1em}<br><br>}<br><br>\underset{k=1}{\overset{m}{\sum <br><br>}}<br><br>{\left[g<br><br>\left(c+k,j\right)-g<br><br>\left(c,j\right)\right]}^2);<br><br>\mathrm{and}\end{array}$

(iii) interconnecting symmetry point to obtain a symmetry line by computing the least squares fitting on data tuples (j,C_j(j)) and associated measurement error value (1−

R(j)), wherein R(j) is a reliability measure for each of the symmetry points.

13. Method of determining a symmetry line in at least one of a horizontal direction and a vertical direction in a radiation image that is represented by a matrix of digital pixel values, comprising the steps of:

(i) calculating, in case of horizontal direction, a symmetry point for each column of the image, and, in case of vertical direction, a symmetry point for each row of the image;

(ii) computing a reliability measure R(c, j) associated with a calculated symmetry point c for column j or row j, respectively, according to;

$R<br><br>\left(c,j\right)=1-\frac{1}{\sqrt{{\mathrm{\sigma <br><br>}}^2<br><br>\left(c,j\right)+1}},<br><br>\mathrm{where}$$\begin{array}{c}{\mathrm{\sigma <br><br>}}^2<br><br>\left(c,j\right)=\text{\hspace{1em}<br><br>}<br><br>\frac{1}{m}<br><br>(\underset{k=1}{\overset{m}{\sum <br><br>}}<br><br>{\left[g<br><br>\left(c-k,j\right)-g<br><br>\left(c,j\right)\right]}^2+\\ \text{\hspace{1em}<br><br>}<br><br>\underset{k=1}{\overset{m}{\sum <br><br>}}<br><br>{\left[g<br><br>\left(c+k,j\right)-g<br><br>\left(c,j\right)\right]}^2);<br><br>\mathrm{and}\end{array}$

(iii) interconnecting symmetry point to obtain a symmetry line by computing the least squares fitting on data tuples (j,C_j(j)) and associated measurement error value (1−

R(j)), wherein R(j) is a reliability measure for each of the symmetry points.

14. Method according to claim 13 wherein a symmetry point for column j or row j, respectively, is obtained by:

(1) calculating for column j or row j, and for each pixel c at position i in column j or row j, symmetrical difference sum values S according to the formula;

$S<br><br>\left(i=c,j\right)=\underset{k=1}{\overset{m<br><br>\left(i\right)}{\sum <br><br>}}<br><br>[g<br><br>\left(c+k,j\right)-{\left(g<br><br>\left(c-k,j\right)\right]}^2,$

 

where c=T, . . . , M−

T−

1, g(i, j) is a gray value at position (i, j), T is an offset parameter, M is a number of rows or columns, respectively in the matrix, and m(i) equals to min (i, M−

i−

1),

(2) normalizing S to obtain {overscore (S)}, and

(3) determining a minimal value {overscore (S)}_min of the values {overscore (S)} obtained for each pixel c, and denoting a value c for which {overscore (S)} is equal to {overscore (S)}_min as the symmetry point of column j or row j, respectively.

15. Method according to claim 13 wherein a horizontal symmetry index (SI_h) is calculated as ${\mathrm{SI}}_h=\frac{1}{N}$

∑

j=0N-1

Sh

(j),

and a vertical symmetry index (SI_v) is calculated as ${\mathrm{SI}}_v=\frac{1}{M}<br><br>\underset{j=0}{\overset{M-1}{\sum <br><br>}}<br><br>S_v<br><br>\left(i\right),$

wherein a main orientation index SI of the image is determined as

16. Method according to claim 13 wherein an orientation angle of the image is determined as an angle between a horizontal coordinate axis and a vertical coordinate axis.