Image enhancement techniques have been widely used in the field of radiology, where the subjective quality of images is important for human interpretation and diagnosis. Contrast is an important factor in subjective evaluation of image quality. Many algorithms for accomplishing contrast enhancement have been developed and applied to problems in medical imaging. A comprehensive survey of several methods has been published by Wang et al. . Among the various techniques published, histogram modification and edge enhancement techniques have been most commonly used along with traditional methods of image processing.
Histogram modification techniques [2,3], explained in Chapter 1, are attractive because of their simplicity and speed and have achieved acceptable results for some applications. The transformation function used is derived from a desired histogram and the histogram of an input image. In general, the transformation function is nonlinear. For continuous functions, a lossless transformation may be achieved. However, for digital images with a finite number of gray levels, such a transformation results in information loss due to quantization. For example, a subtle edge may be merged with its neighboring pixels and disappear. Attempts to incorporate local context into the transformation process have achieved limited success. For example, simple adaptive histogram equalization  supported by fixed contextual regions cannot adapt to features of different size.
Most edge enhancement algorithms share a common strategy implicitly: detection followed by local "edge sharpening." The technique of unsharp masking, discussed in Chapter 2, is significant in that it has become a popular enhancement algorithm to assist the radiologist in diagnosis [5,6]. Unsharp masking sharpens edges by substracting a portion of a filtered component from an original image. Theoretically, this technique was justified as an approximation of a deblurring process by Rosenfeld and Kak . Loo et al.  studied an extension of this technique in the context of digital radiographs. Another refinement based on Laplacian filtering was proposed by Neycenssac . However, techniques of unsharp masking remain limited by their linear and single-scale properties and are less effective for images containing a wide range of salient features, as typically found in digital mammography. In an attempt to overcome these limitations, a local contrast measure and nonlinear transform functions were introduced by Gordon and Rangayyan , and later refined
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by Beghdadi and Negrate . Limitations remained in these nonlinear methods, since no explicit noise suppression stage was included (in fact, noise could be amplified), and ad-hoc nonlinear transform functions were introduced without an analytical basis for their enhancement mechanisms or their potential for artifacts.
Recent advancement of wavelet theory has sparked the interest of researchers in the application of image contrast enhancement [12-18]. In this chapter, we give a detailed mathematical analysis of a dyadic wavelet transform and reveal its connection to the traditional method of unsharp masking. In addition, we discuss a simple nonlinear enhancement function and analyze the problem of introducing artifacts as a result of nonlinear processing of wavelet coefficients. We also describe a denoising strategy that preserves edges using wavelet shrinkage  and adaptive thresholding.
Selected enhancement techniques are discussed in the following sections of this chapter: Section 2 presents a one-dimensional (1D) dyadic wavelet transform. Section 3 analyzes linear enhancement and its mathematical connection to traditional unsharp masking. Section 4 analyzes simple nonlinear enhancement by pointwise functional mapping. Section 5 introduces denoising with wavelet shrinkage along with an adaptive approach for finding threshold values. Section 6 presents a two-dimensional (2D) extension for digital mammography and special procedures developed for denoising and enhancement that avoid orientation distortions. Section 7 presents some sample experimental results and comparisons with existing techniques. Finally, Section 8 concludes our discussion and suggests possible future directions of research.
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