Method for learning-based object detection in cardiac magnetic resonance images

• US 20030035573A1
• Filed: 12/20/2000
• Published: 02/20/2003
• Est. Priority Date: 12/22/1999
• Status: Abandoned Application

• Current Assignee: Siemens Corporate Research Incorporated (Siemens AG)
• Original Assignee: Siemens Corporate Research Incorporated (Siemens AG)
• Inventors: Jolly, Marie-Pierre, Duta, Nicolae
• Application Number:
  US09/741,580
• Publication Number:
  US 20030035573A1
• Time in Patent Office: Days
• US Class Current: 382/128
• CPC Class Codes: G06F 18/00 Pattern recognition
• CPC Class Codes: G06F 18/295 Markov models or related models, e.g. semi-Markov models; Markov random fields; Networks embedding Markov models
• CPC Class Codes: G06T 2207/10088 Magnetic resonance imaging [MRI]
• CPC Class Codes: G06T 2207/20081 Training; Learning
• CPC Class Codes: G06T 2207/30048 Heart; Cardiac
• CPC Class Codes: G06T 7/11 Region-based segmentation
• CPC Class Codes: G06T 7/143 involving probabilistic approaches, e.g. Markov random field [MRF] modelling

Abstract

An automated method for detection of an object of interest in magnetic resonance (MR) two-dimensional (2-D) images wherein the images comprise gray level patterns, the method includes a learning stage utilizing a set of positive/negative training samples drawn from a specified feature space. The learning stage comprises the steps of estimating the distributions of two probabilities P and N are introduced over the feature space, P being associated with positive samples including said object of interest and N being associated with negative samples not including said object of interest; estimating parameters of Markov chains associated with all possible site permutations using said training samples; computing the best site ordering that maximizes the Kullback distance between P and N; computing and storing the log-likelihood ratios induced by said site ordering; scanning a test image at different scales with a constant size window; deriving a feature vector from results of said scanning; and classifying said feature vector based on said best site ordering.

Claims

1. An automated method for detection of an object of interest in magnetic resonance (MR) two-dimensional (2-D) images wherein said images comprise gray level patterns, said method including a learning stage utilizing a set of positive/negative training samples drawn from a specified feature space, said learning stage comprising the steps of:

estimating the distributions of two probabilities P and N are introduced over the feature space, P being associated with positive samples including said object of interest and N being associated with negative samples not including said object of interest;

estimating parameters of Markov chains associated with all possible site permutations using said training samples;

computing the best site ordering that maximizes the Kullback distance between P and N using simulated annealing;

computing and storing the log-likelihood ratios induced by said site ordering;

scanning a test image at different scales with a constant size window;

deriving a feature vector from results of said scanning; and

classifying said feature vector based on said best site ordering.

2. An automated method for detection of an object of interest in accordance with claim 1 wherein said step of computing the best site ordering comprises the steps of:

for each feature site s_i, estimating P(X_si=v) and N(X_si=v) for vε

{0 . . . GL-1} (GL=number of gray levels) and computing the divergence H<sub>P∥

N</sub>(X_si),

for each site pair (s_i,s_j), estimating P(X_si=v₁,X_sj=v₂), N(X_si=v₁,X_sj=v₂), P(X_si=v₁|X_sj=v₂), and N(X_si=v₁|X_sj=v₂), for v₁,v₂ε

{0 . . . GL-1} and computing

$H_{P<br><br><br><br>N}<br><br>(X_{s_i}<br><br><br><br>X_{s_j})=\underset{x,y=0}{\overset{\mathrm{GL}-1}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>P_X<br><br>\left(X=x,Y=y\right)<br><br>\ln <br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{P_X<br><br>\left(X=x<br><br>Y=y\right)}{N_X<br><br>\left(X=x<br><br>Y=y\right)},$

solving a traveling salesman type problem over the sites S to find S*={s₁*, . . . , s_n*} that maximizes H<sub>P∥

N</sub>(X_S),

computing and storing

$L<br><br>\left(X_{s_i^{*}}=v\right)=\ln <br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{P<br><br>\left(X_{s_i^{*}}=v\right)}{N<br><br>\left(X_{s_i^{*}}=v\right)}$

and

$L(X_{s_i^{*}}=v_1<br><br><br><br>X_{s_{i-1}^{*}}=v_2)=\ln <br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{P(X_{S_1^{*}}=v_1<br><br><br><br>X_{s_{i-1}^{*}}=v_2)}{N(X_{s_i^{*}}=v_1<br><br><br><br>X_{s_{i-1}^{*}}=v_2)}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{for}<br><br>\text{\hspace{1em}<br><br>}<br><br>v,v_1,v_2\in <br><br>\left\{0<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{GL}-1\right\}.$

3. An automated method for detection of an object of interest in accordance with claim 1 wherein said step of classifying said feature vector based on said best site ordering comprises:

given S*, the best Markov chain structure and the learned likelihoods L(X_s1*=v) and L(X_si*=v₁∥

X<sub>si−

1</sub>*=v₂) and given a test example O=(o₁, . . . o_n), as preprocessed n-feature vector, then computing the likelihood

$L_o=L<br><br>\left(X_{s_1^{*}}=o_{s_1^{*}}\right)+\underset{i=2}{\overset{n}{\sum <br><br>}}<br><br>L(X_{s_1^{*}}=o_{s_1^{*}}<br><br><br><br>X_{s_{i-1}^{*}}=o_{s_{i-1}^{*}}),$

and if L_o>

T then classifying O as “

object of interest”

else classifying it as “

non object of interest”

.

4. An automated method for detection of an image portion of interest of a cardiac image in magnetic resonance (MR) two-dimensional (2-D) images wherein said images comprise gray level patterns, said method including a learning stage utilizing a set of positive/negative training samples drawn from a specified feature space, said learning stage comprising the steps of:

sampling a plurality of linear cross sections through said image portion of interest and its immediate neighborhood along defined main directions;

subsampling each of said plurality of linear cross sections so as to contain a predetermined number of points;

normalizing the values of said predetermined number of points in a predefined range;

estimating the distributions of two probabilities P and N are introduced over the feature space, P being associated with positive samples including said image portion of interest and N being associated with negative samples not including said image portion of interest;

estimating parameters of Markov chains associated with all possible site permutations using said training samples;

computing the best site ordering that maximizes the Kullback distance between P and N;

computing and storing the log-likelihood ratios induced by said site ordering;

scanning a test image at different scales with a constant size window;

deriving a feature vector from results of said scanning; and

classifying said feature vector based on said best site ordering.

5. An automated method for detection of an image portion of interest in accordance with claim 4 wherein said step of computing the best site ordering comprises the steps of:

for each feature site s_i, estimating P(X_si=v) and N(X_si=v) for vε

{0 . . . GL-1} (GL=number of gray levels) and computing the divergence H<sub>P∥

N</sub>(X_si),

for each site pair (s_i,s_j), estimating P(X_si=v₁,X_sj=v₂), N(X_si=v₁,X_sj=v₂), P(X_si=v₁|X_sj=v₂) and N(X_si=v₁|X_sj=v₂), for v₁,v₂ε

{0 . . . GL-1} and computing

$H_{P<br><br><br><br>N}(X_{s_i}<br><br><br><br>X_{s_j})=\underset{x,y=0}{\overset{\mathrm{GL}-1}{\sum <br><br>}}<br><br>P_X<br><br>\left(X=x,Y=y\right)<br><br>\ln <br><br>\frac{P_X(X=x<br><br><br><br>Y=y)}{N_X(X=x<br><br><br><br>Y=y)},$

solving a traveling salesman type problem over the sites S to find S*={s₁*, . . . , s_n*} that maximizes H<sub>P∥

N</sub>(X_S),

computing and storing

$L<br><br>\left(X_{s_1^{*}}=v\right)=\ln <br><br>\frac{P<br><br>\left(X_{s_i^{*}}=v\right)}{N<br><br>\left(X_{s_1^{*}}=v\right)}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>L(X_{s_i^{*}}=v_1<br><br><br><br>X_{s_{i-1}^{*}}=v_2)=\ln <br><br>\frac{P(X_{s_i^{*}}=v_1<br><br><br><br>X_{s_{i-1}^{*}}=v_2)}{N(X_{s_i^{*}}=v_1<br><br><br><br>X_{s_{i-1}^{*}}=v_2)}$

for v,v₁,v₂ε

{0 . . . GL-1}.

6. An automated method for detection of an image portion of interest in accordance with claim 4 wherein said step of classifying said feature vector based on said best site ordering comprises:

given S*, the best Markov chain structure and the learned likelihoods L(X_si*=v) and L(X_si*=v₁∥

X<sub>si−

1</sub>*=v₂) and given a test example O=(o₁, . . . o_n), as preprocessed n-feature vector, then computing the likelihood

$L_o=L<br><br>\left(X_{s_1^{*}}=o_{s_1^{*}}\right)+\underset{i=2}{\overset{n}{\sum <br><br>}}<br><br>L(X_{s_1^{*}}=o_{s_i^{*}}<br><br><br><br>X_{s_{i-1}^{*}}=o_{s_{i-1}^{*}}),$

and if L_o>

T then classifying O as “

image portion of interest”

else classifying it as “

non image portion of interest”

.

9. An automated method for detection of an image of said flexible object in accordance with claim 4 wherein said step of classifying said feature vector based on said best site ordering comprises:

given S*, the best Markov chain structure and the learned likelihoods L(X_s1*=v) and L(X_si*=v₁|X<sub>si−

1</sub>*=v₂) and given a test example O=(o₁, . . . o_n), as preprocessed n-feature vector, then computing the likelihood

$L_{o<br><br>\text{\hspace{1em}<br><br>}}=L<br><br>\left(X_{s_1^{*}}=o_{s_1^{*}}\right)+\underset{i=2}{\overset{n}{\sum <br><br>}}<br><br>L(X_{s_i^{*}}=o_{s_i^{*}}<br><br><br><br>X_{s_{i-1}^{*}}=o_{s_{i-1}^{*}}),$

and if L_o>

T then classifying O as “

image of said flexible object”

else classifying it as “

non image of said flexible object”

.

7. An automated method for detection of an image of flexible objects, such as a cardiac left ventricle in a cardiac image in magnetic resonance (MR) two-dimensional (2-D) images wherein said images comprise gray level patterns, said method including a learning stage utilizing a set of positive/negative training samples drawn from a-specified feature space, said learning stage comprising the steps of:

sampling four linear cross sections through said image of said flexible object and its immediate neighborhood along defined main directions;

subsampling each of said four linear cross sections so as to contain a predetermined number of points;

normalizing the values of said predetermined number of points in a predefined range;

estimating the distributions of two probabilities P and N are introduced over the feature space, P being associated with positive samples including said image of said of said flexible object and N being associated with negative samples not including said image of said flexible object;

estimating parameters of Markov chains associated with all possible site permutations using said training samples;

computing the best site ordering that maximizes the Kullback distance between P and N;

computing and storing the log-likelihood ratios induced by said site ordering;

scanning a test image at different scales with a constant size window;

deriving a feature vector from results of said scanning; and

classifying said feature vector based on said best site ordering.

8. An automated method for detection of an image portion of interest in accordance with claim 7, wherein said step of computing the best site ordering comprises the steps of:

for each feature site s_i, estimating P(X_si=v) and N(X_si=v) for vε

{0 . . . GL-1} (GL=number of gray levels) and computing the divergence H<sub>P∥

N</sub>(X_si),

for each site pair (s_i,s_j), estimating P(X_si=v₁,X_sj=v₂), N(X_si=v₁,X_sj=v₂), P(X_si=v₁|X_sj=v₂), and N(X_si=v₁|X_sj=v₂), for v₁,v₂ε

{0 . . . GL-1} and computing

$H_{P<br><br><br><br>N}(X_{s_i}<br><br><br><br>X_{s_j})=\underset{x,y=0}{\overset{\mathrm{GL}-1}{\sum <br><br>}}<br><br>P_X<br><br>\left(X=x,Y=y\right)<br><br>\ln <br><br>\frac{P_X(X=x<br><br><br><br>Y=y)}{N_X(X=x<br><br><br><br>Y=y)},$

solving a traveling salesman type problem over the sites S to find S*={s₁*, . . . , s_n*} that maximizes H<sub>P∥

N</sub>(X_S),

computing and storing

$L<br><br>\left(X_{s_1^{*}}=v\right)=\ln <br><br>\frac{P<br><br>\left(X_{s_1^{*}}=v\right)}{N<br><br>\left(X_{s_1^{*}}=v\right)}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>L(X_{s_i^{*}}=v_1<br><br><br><br>X_{s_{i-1}^{*}}=v_2)=\ln <br><br>\frac{P(X_{s_i^{*}}=v_1<br><br><br><br>X_{s_{i-1}^{*}}=v_2)}{N(X_{s_i^{*}}=v_1<br><br><br><br>X_{s_{i-1}^{*}}=v_2)}$

for v,v₁,v₂ε

{0 . . . GL-1}.

10. An automated method for detection of an image of said flexible object in accordance with claim 7, wherein said flexible object is a left ventricle.