Classifying Mammogram Images Using Fractal Features
13 Dec 2007-Vol. 2, pp 537-543
TL;DR: The result has shown the potential usefulness of the fractal signature and fractal dimension for image analysis, and it has been found that 96% classification rate could be achieved in digital mammogram images.
Abstract: Fractal geometry is becoming increasingly important in the study of image characteristics For recognition of regions and object in natural scenes, there is always a need for features, which are invariant and they provide a good set of descriptive values for the region There are numerous methods available to estimate parameters from the image of the fractal surface In this paper, fractal features of digital mammogram images are studied with aim of classifying breast cancer Fractal dimensions(FD) and fractal signature(FS) are considered as different features to characterize the degree of self-similarity among the points in the clusters The result has shown the potential usefulness of the fractal signature and fractal dimension for image analysis The K-Means algorithm is used for classification of images It has been found that 96% classification rate could be achieved Keywords: Fractal dimension, Fractal signature, Mammogram, invariant- methods: data analysis
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TL;DR: The results reveal that fractal based approach is an effective method to improve the skin line segmentation from mammogram images in the computer aided diagnosis.
Abstract: Objective: To develop an algorithm for the identification of breast skin line in mammographic images and evaluate its performance against ground truth images. Methods/Analysis: A three stage processing pipeline was developed to segment the breast skin line. The first part of the segmentation used a pre-processing stage to remove artifacts and reduce image noise. The second stage employed a fractal based approach for segmentation and the third step detects the border region from the segmented image. Findings: The performance of the method has been evaluated using bench mark datasets from MIAS and DDSM. The results of the findings reveal that fractal based approach is an effective method to improve the skin line segmentation from mammogram images in the computer aided diagnosis. The algorithmic results of the segmentation were validated against the ground truth generated by manual segmentation. Improvement: The proposed method shows the importance of fractal analysis for breast skin line segmentation.
4 citations
01 Jan 2009
TL;DR: A fast fractal method to model breast background regions based on entropy, for the detection breast cancer, with a true positive detection rate of 85% was obtained for the 28 abnormal mammograms used.
Abstract: Breast cancer is a leading cause of mortality among women. This paper presents a fast fractal method to model breast background regions based on entropy, for the detection breast cancer. When the modeled mammogram is taken out from the original image the presence of microcalcifications can be enhanced. The tremendous encoding time involved is the major drawback of fractal modeling method. In this paper, the domain pool for searching the matching domain is chosen based on entropy. This reduced the encoding time by a factor of 3.12 when compared with the conventional fractal encoding method which searched the entire domain pool for a matching domain. The average correlation and mean square error between the original and modeled image was obtained as 0.9737 and 5.469 respectively. The method is validated using the mammograms obtained from the MIAS database. A true positive detection rate of 85% was obtained for the 28 abnormal mammograms used.
2 citations
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TL;DR: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster which can be used to infer the appropriateness of data partitions.
Abstract: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster. The measure can be used to infer the appropriateness of data partitions and can therefore be used to compare relative appropriateness of various divisions of the data. The measure does not depend on either the number of clusters analyzed nor the method of partitioning of the data and can be used to guide a cluster seeking algorithm.
6,757 citations
Journal Article•
6,667 citations
TL;DR: The general problem of estimating the a posteriori probabilities of the states and transitions of a Markov source observed through a discrete memoryless channel is considered and an optimal decoding algorithm is derived.
Abstract: The general problem of estimating the a posteriori probabilities of the states and transitions of a Markov source observed through a discrete memoryless channel is considered. The decoding of linear block and convolutional codes to minimize symbol error probability is shown to be a special case of this problem. An optimal decoding algorithm is derived.
4,830 citations
TL;DR: A new family of convolutional codes, nicknamed turbo-codes, built from a particular concatenation of two recursive systematic codes, linked together by nonuniform interleaving appears to be close to the theoretical limit predicted by Shannon.
Abstract: This paper presents a new family of convolutional codes, nicknamed turbo-codes, built from a particular concatenation of two recursive systematic codes, linked together by nonuniform interleaving. Decoding calls on iterative processing in which each component decoder takes advantage of the work of the other at the previous step, with the aid of the original concept of extrinsic information. For sufficiently large interleaving sizes, the correcting performance of turbo-codes, investigated by simulation, appears to be close to the theoretical limit predicted by Shannon.
3,003 citations
27 Nov 1989
TL;DR: The Viterbi algorithm is modified to deliver the most likely path sequence in a finite-state Markov chain, as well as either the a posteriori probability for each bit or a reliability value, with the aim of producing soft decisions to be used in the decoding of outer codes.
Abstract: The Viterbi algorithm (VA) is modified to deliver the most likely path sequence in a finite-state Markov chain, as well as either the a posteriori probability for each bit or a reliability value. With this reliability indicator the modified VA produces soft decisions to be used in the decoding of outer codes. The inner software output Viterbi algorithm (SOVA) accepts and delivers soft sample values and can be regraded as a device for improving the signal-to-noise ratio, similar to an FM demodulator. Several applications are investigated to show the gain over the conventional hard-deciding VA, including concatenated convolutional codes, concatenation of trellis-coded modulation with convolutional FEC (forward error correcting) codes, and coded Viterbi equalization. For these applications additional gains of 1-4 dB as compared to the classical hard-deciding algorithms were found. For comparison, the more complex symbol-to-symbol MAP, whose optimal a posteriori probabilities can be transformed into soft outputs, was investigated. >
1,848 citations