Color image filters: the vector directional approach Konstantinos N. Plataniotis Dimitrios Androutsos Anastasios N. Venetsanopoulos University of Toronto Department of Electrical and Computer Engineering Toronto, M5S 3G4, Ontario, Canada E-mail:
[email protected]
Abstract. Processing of color image data using directional information has received increased attention lately due to the introduction of the vector directional filters. These rank-ordered type filters utilize the direction of color vectors to enhance, restore and segment color images. First, the different vector directional filters already in use are presented, focusing on their similarities and differences and, second, new adaptive vector directional filters are introduced. Fuzzy as well as nearest neighbor structures are utilized to determine the weights in the proposed adaptive filters. Simulation studies involving color images are used to assess the performance of the different vector directional filters and to compare them with other commonly used nonlinear filters. The simulation studies reported indicate that the new adaptive filters are computationally attractive and have excellent performance. © 1997 Society of PhotoOptical Instrumentation Engineers. [S0091-3286(97)02609-3]
Subject terms: color image processing; multichannel filters; distance criteria; adaptive techniques. Paper 32126 received Dec. 23, 1996; revised manuscript received Apr. 16, 1997; accepted for publication Apr. 16, 1997.
1
Introduction
The amount of research published to date indicates an increasing interest in the area of color image processing. It is widely accepted that color conveys information about the objects in a scene and this information can be used to further refine the performance of an imaging system. However, color image processing has not had the same growth and development as other areas in digital signal processing. The multichannel nature of the color image can be considered as the main reason for the slow development. The international standard CIE 1931 defines color curves based on tristimulus values of human capabilities and conditions of view.1 The basis of the trichromatic theory of color vision is that it is possible to match an arbitrary color by superimposing appropriate amounts of three primary colors. Thus, in the different color spaces, each pixel of an image is represented by three values that can be considered as a vector, transforming the color image to a vector field in which each vector’s direction and length is related to the pixel’s chromatic properties.2 Being a 2-D, three-channel signal, a color image requires increased computation and storage, as compared to a gray-scale image during processing. The most common image processing tasks are noise filtering and image enhancement. These tasks are an essential part of any image processor whether the final image is utilized for visual interpretation or for automatic analysis.1 Numerous filtering techniques have been proposed to date for multichannel image processing. Nonlinear filters applied to images are required to preserve edges and details and remove impulsive and Gaussian noise. It has been recognized by many researchers that vector processing of color images is probably a more effective way to filter out noise and to enhance color images. A very important family Opt. Eng. 36(9) 2375–2383 (September 1997)
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of nonlinear image filters is that based on order statistics ~OS!, with the vector median filter ~VMF! the most commonly used member of the family.3 The operation of such a filter can be described according to some distance criterion, which is applied to the set of input vectors inside a processing window. Let y(x):Z l →Z m , represent a multichannel image and let WPZ l be a window of finite size n ~filter length!. The noisy image vectors inside the window W are denoted as x j , j51,2,...,n. If D(xi ,x j ) is a measure of dissimilarity between vectors xi and x j the scalar quantity. n
d i5
(
j51
D ~ xi ,x j !
~1!
is the distance associated with the noisy vector xi inside the processing window of length n. Assuming that an ordering of the d i d ~ 1 !
