June 18, 2006
June 18, 2006
June 21, 2006
Electrical and Computer
11.1023.1 - 11.1023.13
Probability and Image Enhancement Abstract
We present one of five projects used in our course, Probability with Applications in Electrical Engineering. The course is required for all electrical engineering students and is open to third and fourth year students. The project focuses on the applications of probability to image enhancement using histogram equalization and histogram specification methods. These techniques demonstrate applications of functions of random variables, transformations of random variables, and the generation of random variables from specified distributions. We begin by introducing the continuous random variable transformation and demonstrating the process of transforming any random variable distribution to a uniform distribution through the use of the cumulative density function. We then explore the concept of histogram equalization: how it works, its effects on image contrast, and its applications in image processing and image enhancement. Finally, we generalize the histogram equalization problem by showing how the cumulative density function can be used to specify an arbitrary probability distribution and to transform the image accordingly.
ABET evaluation criteria for electrical engineering programs state “The program must demonstrate that graduates have: knowledge of probability and statistics, including applications appropriate to the program name and objectives; and knowledge of mathematics through differential and integral calculus, basic sciences, computer science, and engineering sciences necessary to analyze and design complex electrical and electronic devices, software, and systems containing hardware and software components, as appropriate to program objectives.”(See http://www.abet.org/criteria.html).
We present one of five projects used in our course, Probability with Applications in Electrical Engineering. The course is required for all electrical engineering students and is open to third and fourth year students. We introduce a way to make this topic more appealing to students. In the latest offering, the four other projects included linear averaging,1 computer networks and simulation,2 frequency response and least-squares estimation,1 and conditional probability and receivers in communication systems1.
The project focuses on the applications of probability to image enhancement using both histogram equalization and histogram specification methods. The histogram equalization technique directly uses the original image pixel values to compute the enhanced image’s pixel values. Histogram equalization is widely used in medical image processing, facial recognition, radar, and photo processing software. Image enhancement techniques demonstrate applications of functions of random variables (transformations of random variables, derived random variables) and the generation of random variables from specified distributions. Image processing examples are good in the sense of yielding immediate visual feedback; in addition, students may already have had experience with image editing software.
Aburdene, M., & Goodman, T. (2006, June), Probability And Image Enhancement Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--18
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