Translation and rotation of binary images encoded as minimized Boolean functions

doi:10.1016/S0167-8655(97)00002-0

Pattern Recognition Letters

Volume 18, Issue 2, February 1997, Pages 157-163

https://doi.org/10.1016/S0167-8655(97)00002-0 Get rights and content

Abstract

In the scheme for representing binary images (Sarkar, 1996a), the image was considered as a map of a Boolean function which was minimized to obtain the prime implicants to represent the image. Such a scheme was shown to achieve a drastic saving of storage compared to Linear Quadtrees and Interpolation-based Binary Trees. In this paper we present procedures for translating and rotating an image represented by the above mentioned scheme. The computational complexities of the algorithms are also discussed.

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Cited by (8)

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Citation Excerpt :
Breast cancer is the leading cancer type diagnosed in women; one in eight women is at risk of developing breast cancer throughout their lives [2]. Studies have been carried out on minimization method for Boolean functions [3–13] and on expert systems with Reduced Rule Base [14–21]. Similar studies have been reported on developing medical expert systems [22–33], and their use in medicine [34–38].
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More accurate results were obtained considering all the possibilities related to cancer. Thirteen different risk factors were determined to determine the type of cancer. The truth table produced in our study has 13 inputs and 4 outputs. The Boolean Function Minimization method is used to obtain less situations by simplifying logical functions. Diagnosis of cancer quickly thanks to control of the simplified 4 output functions.
Diagnosis made with the 4 output values obtained using Reduced Rule Base was found to be quicker than diagnosis made by screening all 2¹³= 8192 possibilities. With the improved MES, more probabilities were added to the process and more accurate diagnostic results were obtained. As a result of the simplification process in breast and renal cancer diagnosis 100% diagnosis speed gain, in cervical cancer and lung cancer diagnosis rate gain of 99% was obtained.
With Boolean function minimization, less number of rules is evaluated instead of evaluating a large number of rules. Reducing the number of rules allows the designed system to work more efficiently and to save time, and facilitates to transfer the rules to the designed Expert systems. Interfaces were developed in different software platforms to enable users to test the accuracy of the application. Any one is able to diagnose the cancer itself using determinative risk factors. Thereby likely to beat the cancer with early diagnosis.
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Operations on binary images represented by interpolation based bintrees
1999, Pattern Recognition Letters
The interpolation-based binary tree (IBB) is a set of codes type of encoding scheme for representing binary images, which leads to a considerable amount of storage-saving. In this paper, we present computational techniques for finding the number of black pixels and the centroid of the image represented by the IBB method and the algorithms for various operations like translation, rotation and mirroring of such binary images. The computational complexities of the algorithms are also discussed.
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This paper presents a bibliography of nearly 1700 references related to computer vision and image analysis, arranged by subject matter. The topics covered include computational techniques; feature detection and segmentation; image and scene analysis; two-dimensional shape; pattern; color and texture; matching and stereo; three-dimensional recovery and analysis; three-dimensional shape; and motion. A few references are also given on related topics, including geometry and graphics, compression and processing, sensors and optics, visual perception, neural networks, artificial intelligence and pattern recognition, as well as on applications.
Operations on binary images encoded as minimized Boolean functions
1997, Pattern Recognition Letters
A novel scheme has been devised to represent binary images as minimized Boolean functions. The blocks corresponding to the essential prime implicants are stored as ternary numbers. The scheme has been shown to be simple and very much storage-saving. Based on this new scheme, the present paper describes the formulæ, computational techniques and algorithms of various set operations (viz. intersection, union, complement) and geometric operations (viz. area and centroid) on binary images. The computational complexities of the algorithms are also discussed.
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¹: On summer training from Department of Electrical Engineering, Indian Institute of Science, Bangalore 560012, India.

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Pattern Recognition Letters

Translation and rotation of binary images encoded as minimized Boolean functions

Abstract

An expert system design to diagnose cancer by using a new method reduced rule base

Displacement BDD and geometric transformations of binary decision diagram encoded images

Operations on binary images represented by interpolation based bintrees

Image Analysis and Computer Vision: 1997

Operations on binary images encoded as minimized Boolean functions

Translation and orthogonal rotation of BDD encoded image