Median Based Principal Component Analysis for Edge Detection on Color Images Using Partial Derivatives of Boolean Functions and a New Correlated Color Similarity Measure.

The demand of color image processing is rapidly growing with the increased use of digital cameras and the internet. Applications of color images range from countless personal used to medicine, defense and security. Color images are more suitable for the human eye than gray scale images because humans can distinguish only approximately about twenty four shades of gray whereas they can see thousands of color shades. This work will develop methods for color edge detection for image processing applications and metrics to evaluate the similarity between color images. The two general approaches taken for edge detection that will be investigated here are monochromatic edge detection and vector based edge detection. The first method involves processing each color component individually and then forming a final result via a fusion method. The second method involves analyzing each individual pixel value, as a vector. Both of these methods are straightforward to implement and analyze, making the models suitable for real time operations and inexpensive in hardware. We will test both of these methods on a variety of different color spaces to identify which color space works best for edge detection. A traditional method for color edge detection is to convert color images to grayscale thus utilizing existing edge detection methods. The biggest challenge in this approach is being able to preserve as much edge information as possible during this conversion. This thesis will present a new color space, which is an improved version of the original principal component analysis algorithm. We will show that this new color space is able to better show edges than its original form. Another common form of signal processing which is preformed on color images includes segmentation and data retrieval for recognition systems. For this to be done properly, a robust similarity measure has to be used. Unlike most of the methods that are currently available for this task, the new proposed method is based on the correlation of information between color planes and principal component analysis conversion of a color image into grayscale. This new measure is able to better analyze the similarity of color images. Also, a new complete system for color edge detection based on this principle is developed and presented. This innovative design utilizes partial derivatives of Boolean functions for edge detection. Analysis will be preformed using our new measure. Quantitative and qualitative results testing the scheme on a database of natural and synthetic images will demonstrate the performance of the algorithms to be comparable, if not better, then other current state of the art methods.