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Color Image Filtering and Enhancement - Fundamentals of Color Imaging, Noise Modeling, Image Filtering Basics

vector processing filters figure

Rastislav Lukac, Konstantinos N. Plataniotis, and Anastasios N. Venetsanopoulos
University of Toronto, Toronto, Canada

Definition: Color image filtering and enhancement refer to the process of noise reduction in the color image and enhancement of the visual quality of the image input.

Noise encountered into the image data reduces the perceptual quality of an image and thus limits the performance of the imaging system. The generation of high quality color images which are visually pleasing is of great importance in a variety of application areas. That pre supposes image filtering, since images captured with sensing devices and transmitted through communication networks are often corrupted by noise. Therefore, both filtering and enhancement constitute an important part of any image processing pipeline where the final image is utilized for visual inspection or for automatic analysis.

The filtering operators applied to color images are required to preserve color information and structural content (edges and fine details), and to remove noise. The choice of these criteria follows the well-known fact that the human visual system is sensitive to changes in color appearance and fine details. Further to that, a good filtering/enhancement method should maintain the edge information while it removes image noise. Edges are important features since they indicate the presence, and the shape, of various objects in the image. From this viewpoint it is evident that the noise removal task in digital color imaging may be viewed as compromise between the noise suppression and color/structural content preservation.

Fundamentals of Color Imaging

Following the tristimulus theory of color representation, each pixel in a color Red-Green-Blue image (Figure 2) can be viewed as a three-component vector x i = [ x i 1 , x i 2 , x i 3 ] in the color RGB space (Figure 3). Thus, the color image is a vector array or a two-dimensional matrix of three-component samples x i with x ik denoting the R ( k = 1), G ( k = 2) or B ( k = 3) component (Figure 2). The chromaticity properties of color vector x i relate to its magnitude and direction (orientation in the vector space) which respectively relate to the luminance and chromaticity characteristics of the color pixel. Since both these measures are essential for human perception, color image processing techniques should preserve the color vectors’ characteristics during processing. The processing operations can be performed in the magnitude domain, directional domain, or ideally both magnitude and directional information should be taken into consideration in outputting the color image with enhanced visual quality

Noise Modeling

Noise in digital images can be introduced by numerous sources, with the most common of them listed in Figure 4, and is present in almost any image processing system. Based on the difference between the observation (noisy) color vector x i = [ x i 1 , x i 2 , x i 3 ] and the original (desired) sample o i =[ o i 1 , o i 2 , o i 3 ], the noise corruption is modeled via the additive noise model x i = o i + v i with v i =[ v i 1 , v i 2 , v i 3 ] denoting the vector which describes the noise process. The noise contribution v i can describe either signal-dependent or independent noise.

Given the definition above, color noise is the amount of color fluctuation given a certain color signal. As such the color noise signal should be considered as a three-channel perturbation vector in the RGB color space, affecting the spread of the actual color vectors in the space

Image Filtering Basics

Noise reduction techniques are most often divided into two classes linear techniques, and nonlinear techniques. Linear processing techniques have been widely used in digital signal processing applications, since their mathematical simplicity and the availability of a unifying linear system theory make these techniques relatively easy to analyze and implement. However, most of the linear techniques tend to blur structural elements such as lines, edges and other fine image details. Since image signals are nonlinear in nature due to the presence of structural information and are perceived via the human visual system which has strong nonlinear characteristics, nonlinear filters can potentially preserve important multichannel structural elements, such as color edges and eliminate degradations occurring during signal formation or transmission through nonlinear channel.

Since natural images should be considered non-stationary signals due to presence of edges, varying color information and noise, filtering schemes operate on the premise that an image can be subdivided into small regions, each of which can be treated as stationary. Most color filtering techniques operate on some type of sliding window placing the pixel x ( N +1)/2 under consideration at the center of the processing window (Figure 5). This pixel’s value is changed as a result of a filtering operation on the vectors x 1 , x 2 ,x N included in a local neighborhood. This window operator slides over the entire image successively placing each image pixel at its center (Figure 5).

The performance of a filtering scheme is generally influenced by the size of the local area inside the processing window. Some applications may require larger support to read local image features and complete the task appropriately. On the other hand, a filter operating on a smaller spatial neighborhood can better match image details. The most commonly used window is a 3×3 square shape (Figure 5) due to its versatility and performance, however, a particular window, such as those presented in can be designed to preserve specifically oriented image edges.

Component-wise vs. Vector Color Image Filtering

Since each individual channel of a color image can be considered a monochrome (gray-scale) image (Figure 2), traditional image filtering techniques such as well-known (scalar) median filters often involved the application of scalar filters on each channel separately (Figure 6a). However, this disrupts the correlation that exists between the color components of natural images represented in a correlated color space, such as RGB or its standardized variants. Given the fact that each processing step is usually accompanied by a certain inaccuracy, the formation of the output color vector from the separately processed color components usually produces color artifacts.

It is believed that vector filtering techniques that treat the color image as a vector field (Figure 6b) are more appropriate for color image processing. With such an approach, the filter output is a function of the vectorial inputs x 1 , x 2 ,x N , located within the supporting window (Figure 5). The two basic classes of vector filters are constituted by vector median related filters vector directional filters.

The vector median filter (VMF) is a vector processing operator which has been introduced as an extension of the scalar median filter. The VMF output is the sample (lowest ranked vector or lowest order statistics) x (1) { x 1 , x 2 , x N } that minimizes the distance to the other samples inside the processing window as follows:

where L is the Minkowski metric used to quantify the distance between two color pixels x i and x j in the magnitude domain. Since the above concept can be used to determine the positions of the different input vectors without any a priori information regarding the signal distributions, VMF-related filters are robust estimators.

Vector directional filters operate on the directions of image vectors, aiming at eliminating vectors with atypical directions in the color space. The output of the basic vector directional filter (BVDF) is the sample (lowest ranked vector or lowest order statistics) x (1) ? { x 1 , x 2 , x N } which minimizes the angular ordering criteria to other samples inside the sliding filtering window:

where A(·,·) denotes the angle (angular distance) between two color vectors. Thus, the VDF filters do not take into account the brightness of color vectors. To utilize both features in color image filtering, the generalized vector directional filters (GVDF) and double window GVDF first eliminate the color vectors with atypical directions in the vector space and subsequently process the vectors with the most similar orientation according to their magnitude. In this way, the GVDF splits the color image processing into directional processing and magnitude processing .

The traditional VMF and VDF filters do not take into account neither the importance of the specific samples in the filter window or structural contents of the image. Better performance can be obtained when distances are appropriately modified by weighting coefficients representing the degree to which each input vector contributes to the output of the filte or of which the specific distances between multichannel inputs contribute to the aggregated measure serving as an ordering criterion . Such an idea is behind the weighted vector filters such as weighted VMFs, weighted VDFs and fuzzy-weighted VDFs. The selection weighted vector filters in allow for the simultaneous utilization of both the magnitude and directional characteristics of the color vectors, and generalize a number of previous filtering techniques including VMF, BVDF and their weighted modifications.

To adapt the filter weights (or parameters in general) to varying signal and noise statistics, different multichannel adaptation algorithms can be utilized The achieved weights should be sufficiently robust and their utilization should lead to the essential trade-off between noise smoothing and signal-detail preservation (Figure 8).

Switching Vector Filters

Traditional filtering schemes such as VMF and BVDF which operate on a fixed supporting window introduce excessive smoothing, blur edges and eliminate fine image details. This effect should be attributed to the low-pass filtering characteristics of these color image filters. To prevent excessive smoothing and preserve fine image details, one of the most popular and computationally efficient solutions switch between a robust nonlinear smoothing mode and an identity processing mode which leaves input samples unchanged during the filtering operation (Figure 9) Such an approach allows for the fast adaptation of the filter behavior to the statistics of the input image and it usually leads to an excellent performance in the environments with impulsive-type noise.

Emerging Applications

Robust performance characteristics and a trade-off between noise suppression and color/structural information preservation are often required in real-life imaging applications where inputs are often corrupted by noise or other visual impairments. Emerging applications include, but not limited to, virtual restoration of artworks and enhancement of the digitized images in digital artwork libraries, reconstruction of television images and old movies, microarray image processing and many others. The appearance of the noise as well as useful color/structural image information differs between the applications and thus, the designer should take into consideration the specifics of each application.

For example, strong color/structural preserving characteristics are required in the virtual restoration of artworks (Figure 10). In this application, noise is introduced by scanning the granulated, dirty, or damaged surface of the original artworks. To produce visually pleasing enhanced image with removed outliers and sharply looking fine details, adaptive vector filters should be used. On the other hand, cDNA microarray image processing (Figure 11) may require the utilization of robust processing techniques such as the vector order-statistics filters or the vector fuzzy filters , which are capable to preserve the spot information and eliminate substantial noise floor in the two-channel cDNA image data.

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