Faculty of Computer Science Information Theoretic Measures: Object Segmentation and Tracking CMPUT 615 Nilanjan Ray © 2007
Information Theory • Information theory refers to quantification of “information” • Gained prominence and attention by Shannon in 1948 • Modern computers and communication systems have their deep roots in information theory • Found numerous applications – coding, wireless, statistical inference, natural language processing, cryptography, image analysis, and many other areas 2
Information Entropy • One of the basic notions in information theory pi is a probability mass function 3
Information Divergence Measures • Compares two probability mass/density functions • Various divergence measures exists– KL divergence, Jdivergence, Bhattacharya coefficient, etc. • Found applications in – – – Image registration Object segmentation Object classification Object tracking … 4
Automated Tumor Segmentation from MRI • Automated and accurate tumor boundary delineation is an extremely complex, nontrivial task that should use wealth of information, not just images! • Significant for several reasons, among them: – Clinical applications: diagnosis, drug response, informatics, MR image database indexing according to location, size etc. – Medical research: tumor growth prediction, drug discovery, … MRI Scan 5
Toward Tumor Segmentation: Locating A Fast Bounding Box • As an important step toward automated tumor boundary delineation, we propose a real-time and convenient method to find a bounding box around an anomalous region (e. g. , tumor or edema) on MRI scan • An initial step toward tumor boundary delineation • Can help medical informatics: real-time image database indexing based on tumor position, size, shape, etc. 6
Locating a Bounding Box… Problem definition: Finding an anomalous region D in image I using reference image R D Image I Reference Image R To detect D from I using R: Straightforward, fast techniques such as edge detection, point-wise subtraction often do not work for brain MRI Unsupervised techniques, such as snakes, level set methods may be insufficient, typically require a lot of tuning parameters, and can be slow Supervised techniques, such as pixel classifications, require training sets, often need image registration (non-trivial), and can be slow We propose a fast method, where the only tuning parameter is the number of feature histogram bins. No training data needed. No registration required. Uses single MRI slice, so independent of intensity variation among MR slices. 7
Our Approach: Image Analysis Perspective 0, 0 w T = top portion s B = bottom portion D h I R We propose a score metric based on Bhattacharya coefficient between feature probabilities (normalized histograms) of I and R: where Claim: We can show that if the feature histogram within D is sufficiently different from that outside Dthe plot of E(s) vs. s would look like: E(s) Incr. 0 Decr. s Incr. h We need two 1 D score metric plots to find the dissimilar region D 8
FBB: Locating Brain Tumor Fig. 2: Locating brain anomaly. Use (approximate) symmetry of brain to get reference image and test image The method can tolerate a reasonable shift of line of symmetry and rotation of the head, 9 because it makes use of region-based symmetry, rather than point-wise symmetry
More Visual Examples MRIs and bounding boxes using proposed method 10
Visual Comparison Fig. 3: Top row: results of the proposed FBB technique. Bottom row: results of Chan – Vese bounding box algorithm (CVBB). 11
Numerical Comparison Dice Coefficient MRI slice number Dice coefficients for MRI slices. Solid line denotes FBB algorithm, dotted lines denote CVBB. where G is the set of the tumor pixels found by a radiologist and S is set of pixels found by the proposed algorithm. 12
From Bounding Box toward Boundary: An Example Bounding box by Proposed Method Chan-Vese level set method within bounding box Chan-Vese level set method without bounding box 13
Future Plans • Extensive testing on Alberta Cross Cancer Institute image database • Incorporation as a pre-processing step at in-house segmentation algorithms (visit: http: //www. cs. ualberta. ca/~btgp/) • Extension to 3 D: should need 3 score metric plots • A general image analysis technique: can be applied to suitable applications, such as background subtraction with limited number of frames, jittery environment • Instead of rectangular boxes, can work with general boundaries: level set based framework 14
Summary • Proposed a bounding box locating method around anomaly • Uses region-based left-right symmetry, rather than point-wise symmetry • Uses single MR image • No training data required • No image registration needed • No effect of variability in image intensity across MR images 15
Thanks! A Short Demo Visit brain tumor project page: http: //www. cs. ualberta. ca/~btgp/ 16
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