scar slides

Detection of Cancerous Masses for Screening Mammography using DWT based Multiresolution Markov Random Field: 

Detection of Cancerous Masses for Screening Mammography using DWT based Multiresolution Markov Random Field Lei Zheng, Andrew K. Chan, Gary McCord*, Steve Wu+, J. Steve Liu+ Department of Electrical Engineering *Department of Anatomy + Department of Computer Science Texas A&M University College Station, Texas 77845

Slide2: 

Objective: Develop algorithms for assisting radiologists to locate regions suspected of cancer in a mammograms. Method: Mammogram Segmentation: Use fractal analysis and DWT(Discrete Wavelet Transform) based MRF(Markov Random Field) for image segmentation. Classification: Extract target features from segmentation results before using Binary Logic Decision Tree to identify suspected cancerous masses.

Slide3: 

classification Fractal Analysis DWT based MMRF segmentation

Fractal Analysis of the Mammogram: 

Fractal Analysis of the Mammogram Reasons to use Fractal Analysis Discard regions that have either very smooth or very rough texture. Reduce the search region to increase the detection accuracy. Parameters and algorithms involved Fractal dimension D measures the roughness of a given image segment. Blanket algorithm is used to compute the value of D.

Fractal Analysis: 

Fractal Analysis Fractal Dimension D of a n X n segment: Blanket algorithm is used to calculate D: Assume the volume of a graph region is u, and the gray level at (i, j) is p(i, j), then: The blanket volume is then obtained by The blanket surface area at r is: A: area; K: normalizing constant; r: elementary ruler;

Possible locations of Tumor using Fractal Analysis: 

Possible locations of Tumor using Fractal Analysis The original image Blocks that have a fractal value between 2.65~2.7 Possible Tumor

DWT based MRF segmentation DWT decomposes an image into high and low frequency components: 

DWT based MRF segmentation DWT decomposes an image into high and low frequency components 1. The original Image 2. Result of level 1 decomposition 3. Result of level 2 decomposition

DWT based MRF segmentationFilter-bank implementation of DWT: 

DWT based MRF segmentation Filter-bank implementation of DWT

Markov Random Field: 

Markov Random Field It is a numerical technique for image segmentation. It operates on the basis of probability of “likeness.” The probability is increased if the potential function is minimized.

Markov Random Field: 

Markov Random Field Given an observed image Y={yi} ( i=1,2, …,WxL), and WxL is its size). After segmentation, Y is labeled by segmentation result X={xi}. What is the probability of P(X|Y)? (How close is X to the original unpolluted image?) We use MRF to obtain the answer. image Y={yi} image X={xi}

Markov Random Field (continued): 

For a given image Y, the probability for the label X is: To get the optimal solution for X, the U(X|Y) must be the smallest. Markov Random Field (continued)

DWT based MRF segmentationAn overview: 

DWT based MRF segmentation An overview Retain only the LL subbands in a pyramid decomposition of a mammogram. Based on the results of fractal analysis, use dogs & rabbits algorithm to initialize the MRF segmentation at the lowest resolution. Repeat the MRF algorithm for the LL subband at each resolution moving from coarse toward the finer resolutions.

DWT based MRF segmentation: 

DWT based MRF segmentation MRF result propagation between different resolutions

The initialization of MRF segmentation --- Dogs & Rabbits algorithm: 

The initialization of MRF segmentation --- Dogs & Rabbits algorithm Procedures of the Dogs & Rabbits algorithm (1). Initialize K dogs (cluster centers) at random positions. (2). Select a random data point (rabbit) in the data set; (3). Calculate the distance between the rabbit and the dogs to find the closest dog; (4). Move the dogs towards the rabbit according to the dynamic and retarding the movement of the dogs. (5). If the dog is closest to the rabbit, increase the fatigue of the dog; (6). Repeat step 2~5 until a convergence criterion on the dogs has been reached.

MRF InitializationThe Dogs and Rabbits Algorithm: 

MRF Initialization The Dogs and Rabbits Algorithm All data points in an image are the rabbits. We form several cluster centers we call the dogs, The algorithm classifies each data value into one of the dogs based on a given measure.

The initialization of MRF segmentation --- Dogs & Rabbits algorithm: 

The initialization of MRF segmentation --- Dogs & Rabbits algorithm The movement of the closest dog is determined by: The other dogs’ movement: Here, and are the previous and current positions of the dog respectively. D is the Euclidean distance between the current dog and rabbit, and f1 is the fatigue of the dog which determines how much the current dog should move to the appeared data(rabbit). A>0 determines the inhibition of the movement for the other dogs except the one closest to the rabbit.

The segmentation Result: 

The segmentation Result The mammogram is segmented into 12 clusters based on previous experience. Features are extracted from the results of MRF segmentation.

Tumor Classification --- criteria for feature selection: 

Tumor Classification --- criteria for feature selection Area: It equals to the number of pixels within a certain extracted region. Compactness (cmp): It reflects the shape of the given region. Mean gradient within current region (mwg): It measures the average gradient of each pixel in the current region. Mean gradient of region boundary (mg): It measures the sharpness of each region boundary. Gray value variance (var): It measures the smoothness of the extracted region. Edge Distance Variance (edv): This measures the shape of the region and its rotational symmetry. Mean Intensity Difference (diff): This measures the gray value difference between the values inside a given region and those outside the region but inside the smallest rectangle cover the region.

Tumor Classification --- binary decision tree: 

Tumor Classification --- binary decision tree

Location of Malignant and Benign Masses: 

Location of Malignant and Benign Masses Results: Total number of mammograms (MIAS): 322 Average number of suspicious regions per image: Total number of suspicious regions / Total number of images = 1298/322=4.03 Number of False Negatives per image: Total number of undetected positive regions / Total number of images = 1/322=0.00315 Number of False Positives per image: Total number of false alarms / Total number of images = (1298-36)/322 =3.92 Sensitivity: Detected True Positives / Actual number of Positives = 36/37 = 97.30%

Location of Malignant and Benign Masses: 

Location of Malignant and Benign Masses Mdb010-circ. T

Location of Malignant and Benign Masses: 

Location of Malignant and Benign Masses Original Image Detected areas in circles Medically proven malignancy.

Conclusions: 

Conclusions An efficient algorithm has been constructed to assist the detection of cancerous Masses. The algorithm is based on Fractal Analysis, DWT based MRF segmentation, Binary decision Tree. Experimental results support the validity of the algorithm through the processing of a statistically significant data set.