Method and apparatus for contour tracking of an image through a class of non linear filters

• US 7,272,241 B2
• Filed: 09/18/2003
• Issued: 09/18/2007
• Est. Priority Date: 09/18/2002
• Status: Expired due to Fees

• Current Assignee: CNR Consiglio Nazionale Delle Rieerche, Esaote SpA
• Original Assignee: Esaote SpA, Consiglio Nazionale Delle Ricerche (Repubblica Italiana)
• Inventors: Demi, Marcello, Gemignani, Vincenzo, Paterni, Marco, Benassi, Antonio
• Primary Examiner(s): Mehta; Bhavesh M
• Assistant Examiner(s): Carter; Aaron W
• Application Number:
  US10/665,102
• Publication Number:
  US 20040096106A1
• Time in Patent Office: 1,461 Days
• Field of Search: 382/103, 382/199, 382/266, 348169-172
• US Class Current: 382/103
• CPC Class Codes: G06T 2207/10016 Video; Image sequence
• CPC Class Codes: G06T 2207/10072 Tomographic images
• CPC Class Codes: G06T 7/13 Edge detection
• CPC Class Codes: G06T 7/215 Motion-based segmentation
• CPC Class Codes: G06T 7/66 of image moments or centre of gravity

Abstract

A method for automatically detecting and tracking the contour of an image that uses a class of filters, obtained from the first order absolute central moment. The method provides the steps of filtering a starting image through the absolute central moment e(n,m) of the intensity of a pixel of the image, being n and m the coordinates of each pixel, where the absolute central moment is obtained with the following steps: determining for each n,m the local mean calculated in a neighborhood about a pixel of coordinates n,m of the starting image, thus obtaining a first filtered image; determining for each n,m the sum of the absolute differences between the intensity of a pixel of coordinates n,m of the first filtered image and the intensity of all the pixels contained in a neighborhood about a pixel of coordinates n,m of either the starting image or a second filtered image obtained from the starting image.

Claims

1. A method for automatically detecting and tracking the contour of a starting image, said starting image being formed by an array of pixels and each pixel having an intensity, being n and m coordinates of a generic pixel, comprising the steps of:

filtering said starting image through an absolute central moment e(n,m) of the intensity of the pixels of said starting image, wherein said absolute central moment is obtained with the following steps;

determining for each n,m a local mean calculated on a neighborhood about a pixel of coordinates n,m of the starting image, obtaining a first filtered image;

determining for each n,m a sum of absolute differences between the intensity of the pixel having coordinates n,m of the first filtered image and the intensity of all the pixels contained in a neighborhood about said pixel of coordinates n,m of either said starting image or a second filtered image derived from said starting image,

wherein said sum of absolute differences is split calculating a sum of positive differences, or positive deviation, and a sum of negative differences, or negative deviation.

2. Method according to claim 1, wherein said sum of absolute differences is calculated computing the differences between said first filtered image and said second filtered image, wherein said second filtered image is obtained for each n,m from a local mean calculated on a neighborhood about the pixel of coordinates n,m of said starting image.

3. Method according to claim 1, wherein said absolute central moment e(n,m) is calculated in a generalized way as follows:

$\begin{array}{cc}e<br><br>\left(n,m\right)=w_4<br><br>\left(n,m\right)\otimes <br><br>\sum <br><br>\underset{\left(k,l\right)\in <br><br>{\mathrm{\Theta <br><br>}}_3}{\sum <br><br>}<br><br><br><br>{\mathrm{\mu <br><br>}}_1<br><br>\left(n,m\right)-{\mathrm{\mu <br><br>}}_2<br><br>\left(n-k,m-l\right)<br><br><br><br>w_3<br><br>\left(k,l\right)& \left(1\right)\end{array}$

where;

n,m are the coordinates of a pixel of a map f(n,m) of said image;

w₁(n,m), w₂(n,m), w₃(n,m) and w₄(n,m) are four weight functions defined on four circular domains Θ

₁, Θ

₂, Θ

₃ and Θ

₄, each point of said domains having coordinates (k,l), said circular domains Θ

₁, Θ

₂, Θ

₃ and Θ

₄ having respectively radius r₁, r₂, r₃ and r₄ and being defined as

Θ

_i={(k,l)∈

I²;

√

{square root over (k²+l²)}≦

r_i}

{circle around (X)} is a convolution operator;

${\mathrm{\mu <br><br>}}_1<br><br>\left(n,m\right)=\sum <br><br>\underset{\left(k,l\right)\in <br><br>{\mathrm{\Theta <br><br>}}_1}{\sum <br><br>}<br><br>f<br><br>\left(n,m\right)<br><br>w_1<br><br>\left(n,m\right)$

is a mean value on domain Θ

₁ of said map and of said first filtered image;

${\mathrm{\mu <br><br>}}_2<br><br>\left(n,m\right)=\sum <br><br>\underset{\left(k,l\right)\in <br><br>{\mathrm{\Theta <br><br>}}_2}{\sum <br><br>}<br><br>f<br><br>\left(n-k,m-l\right)<br><br>w_2<br><br>\left(k,l\right)$

the mean value on domain Θ

₂ of said map and of said second filtered image.

4. Method according to claim 3, wherein, starting from said absolute central moment e(n,m) calculated in said generalized way, said positive deviation e_p(n,m) and said negative deviation e_n(n,m) are used as further filters, defined as

$\begin{array}{c}\begin{array}{c}{e}_p\end{array}\end{array}$

( n , m ) = w 4 ⁡

( n , m ) ⊗

∑

∑

( k , l ) ∈

Θ

3 ⁢

p ⁢

( μ

1 ⁡

( n , m ) - μ

2 ⁡

( n - k , m - l ) ) ⁢

w 3 ⁡

( k , l ) e n ⁡

( n , m ) = w 4 ⁡

( n , m ) ⊗

∑

∑

( k , l ) ∈

Θ

3 ⁢

n ⁢

( μ

1 ⁡

( n , m ) - μ

2 ⁡

( n - k , m - l ) ) ⁢

w 3 ⁡

( k , l ) ( 7 )

where domains Θ

_3p and Θ

_3n are defined as;

Θ

_3p={(k,l)∈

Θ

₃;

μ

₁(n,m)>

μ

₂(n−

k,m−

l)}

Θ

_3n={(k,l)∈

Θ

₃;

μ

₁(n,m)<

μ

₂(n−

k,m−

l)} 

 

(8).

5. Method according to claim 4, wherein said step of computing the absolute central moment of the intensity of a pixel comprises the steps of:

defining said circular domains Θ

₁, Θ

₂, Θ

₃ and Θ

₄, in a neighborhood about each point of the starting image, wherein Θ

₁, Θ

₃ and Θ

₄ are centered on n,m and Θ

₂ is a domain centered respectively on each point inside Θ

₃;

associating to each domain Θ

_i, with i comprised between 1 and 4, a weight function w_i and computing a mean value μ

_i of a grey levels map for domains Θ

₁ and Θ

₂ on the basis of said w_i;

computing the absolute central moment e(n,m) on the basis of a weight function w₃ on domain Θ

₃;

splitting the absolute central moment e(n,m) into a positive deviation e_p(n,m) and a negative deviation e_n(n,m), thus creating near a discontinuity two partially overlapping bell-shaped profiles;

convoluting said positive deviation e_p(n,m) and said negative deviation e_n(n,m) with weight function w₄ on domain Θ

₄;

measuring said discontinuity using said positive deviation e_p(n,m) and negative deviation e_n(n,m) as filters.

6. Method according to claim 5, wherein said step of measuring discontinuity is carried out by tracking of a function

Min(e_p(n,m),|e_n(n,m)|).

7. Method according to claim 6, wherein said step of measuring discontinuity is carried out through a subtraction defined as:

e(n,m)=e_p(n,m)−

e_n(n,m).

8. Method according to claim 6, wherein a DoG filter (difference of Gaussian curves) is obtained using a sum of said positive e_p(n,m) and negative e_n(n,m) deviations of the absolute central moment e(n,m).

9. Method according to claim 1, wherein said starting images are selected from the group of biomedical imaging techniques consisting of:

ultrasonic pulses, PET, SPECT, CAT, MR, among which anatomical images, or images of function, obtained by means of time sequences of anatomical views of a particular zone of an organ, or perfusion images, obtained on the same organ after treatment of the patient with substances that enhance the perfusion in the organ;

images of graphs acquired by a scanner in order to convert paper graphs into digital signals.

10. Method according to claim 9 wherein, in case of images of graphs, scanned images are filtered with said absolute central moment e(n,m) tracking it as a bell-shaped profile whose peak is the sought digital signal, a further step being provided of computing the digital signal with a local maxima detection algorithm of standard type.

11. Method for contour tracking, according to claim 3, characterized in that at a discontinuity said absolute central moment e(n,m) calculated in said generalized way as

$\begin{array}{c}{e}^{\prime }\end{array}$

⁡

( n , m ) = ∑

∑

( k , l ) ∈

Θ

3 ⁢



μ

1 ⁡

( n , m ) - f ⁡

( n - k , m - l ) 

⁢

w 3 ⁡

( k , l ) ( 12 )

is compared with a threshold value derived from said generalized absolute central moment, calculated as

$\begin{array}{cc}\begin{array}{c}{e}^{\mathrm{″<br><br>}}<br><br>\left(n,m\right)=<br><br>w_4<br><br>\left(n,m\right)\otimes <br><br>\\ <br><br>\sum <br><br>\underset{\left(k,l\right)\in <br><br>{\mathrm{\Theta <br><br>}}_3}{\sum <br><br>}<br><br><br><br>f<br><br>\left(n,m\right)-f<br><br>\left(n-k,m-l\right)<br><br><br><br>w_3<br><br>\left(k,l\right).\end{array}& \left(13\right)\end{array}$

12. Apparatus for contour tracking in video images arranged as succession of photograms, comprising:

an arithmetic logic unit,

one or several filters that calculate a positive deviation e_p(n,m) and a negative deviation e_n(n,m) of an absolute generalized central moment e(n,m)

a calculating means residing in said arithmetic unit for obtaining said absolute generalized central moment e(n,m), wherein said calculating means;

determines for each n,m a local mean calculated on a neighborhood about a pixel of coordinates n,m of the starting image, obtaining a first filtered image;

determines for each n,m a sum of absolute differences between the intensity of the pixel having coordinates n,m of the first filtered image and the intensity of all the pixels contained in a neighborhood about said pixel of coordinates n,m of either said starting image or a second filtered image derived from said starting image,

splits said sum of absolute differences calculating a sum of positive differences, or positive deviation, and a sum of negative differences, or negative deviation.

13. Apparatus according to claim 12, wherein said positive deviation e_p(n,m) and said negative deviation e_n(n,m) are defined as:

$\begin{array}{cc}\begin{array}{c}{e}_p<br><br>\left(n,m\right)=w_4<br><br>\left(n,m\right)\otimes <br><br>\sum <br><br>\underset{\left(k,l\right)\in <br><br>{\mathrm{\Theta <br><br>}}_{3<br><br>p}}{\sum <br><br>}<br><br>\left({\mathrm{\mu <br><br>}}_1<br><br>\left(n,m\right)-{\mathrm{\mu <br><br>}}_2<br><br>\left(n-k,m-l\right)\right)<br><br>w_3<br><br>\left(k,l\right)\\ e_n<br><br>\left(n,m\right)=w_4<br><br>\left(n,m\right)\otimes <br><br>\sum <br><br>\underset{\left(k,l\right)\in <br><br>{\mathrm{\Theta <br><br>}}_{3<br><br>n}}{\sum <br><br>}<br><br>\left({\mathrm{\mu <br><br>}}_1<br><br>\left(n,m\right)-{\mathrm{\mu <br><br>}}_2<br><br>\left(n-k,m-l\right)\right)<br><br>w_3<br><br>\left(k,l\right)\end{array}& \left(7\right)\end{array}$

where domains Θ

_3p and Θ

_3n are defined as;

Θ

_3p={(k,l)∈

Θ

₃;

μ

₁(n,m)>

μ

₂(n−

k,m−

l)}

Θ

_3n={(k,l)∈

Θ

₃;

μ

₁(n,m)<

μ

₂(n−

k,m−

l)} 

 

(8).

14. Apparatus according to claim 12 wherein said filters consist of four bidimensional convolutors and an integrator.

15. Apparatus, according to claim 14, wherein each of said bidimensional convolutors is replaced by a cascade of two monodimensional convolutors.