N 1

For completeness, we mention that the formula of Eq. (14) can be seen as a multiscale and nonlinear extension of the original unsharp masking operator defined by Eq. (9). We argue that multiscale unsharp masking as defined by Eq. (14) makes a marked improvement over traditional techniques in two respects:

1. The fast multiscale (or multimask) decomposition procedure efficiently identifies features existing within distinct levels of scale, eliminating the need for search.

2. The nonlinear algorithm enhances small features within each scale without blurring the edges of larger features, making possible the simultaneous enhancement of features of all sizes.

4.4 Enhancement Techniques

To accomplish multiscale contrast enhancement, nonlinear techniques for image enhancement were applied to levels of a multiresolution representation. For each basis, there were four

components in the transform space: horizontal, vertical, diagonal, and a DC component, represented by ¿1, d2, d3, and s1, respectively; i is the level of a transform. Let s be the original image, g be the function designed to emphasize features of importance within a selected level i, and L be the number of levels in a transform. Then, an enhanced image may be constructed by s = E W-1(g(d1),g(d2),g(d3), s1). (15)

In general, by defining a function g, we can denote specific enhancement schemes for modifying the coefficients within distinct selected levels of scale-space.

Local Enhancement Techniques

Image enhancement should emphasize important features while reducing the enhancement of noise. Enhancement techniques for digital mammography based on multi-scale edges have been developed [12-15]. In this chapter, we will consider the enhancement to be specified by

2it n fd1 (m, n), if: ei(m, n)< Ti d 1(m, n) = < . .

Lgid1 (m, n), if: el(m, n)>Ti, where m and n denote coordinates in the spatial domain, e1 is the edge set corresponding to the transform space component d1, g1 is a local gain, and T1 is a threshold at level i; g1 and T1 are selected adaptively. The edge set ei of d1i contains the local maxima of d1 along the horizontal direction. For d2 and d3, the direction is along the vertical and diagonal orientations (45°), respectively. Specifically,

FIGURE 6 1D contrast enhancement of a synthetic signal (a) by four-level dyadic wavelet analysis with (b) a linear operator with K0 = 2.3, and (c) a nonlinear operator with t = 0.1 and K0 = 7.

0, otherwise.

The processing of d2 and d3 is similar. By simply replacing d1, ¿2, and d3 with corresponding modified components d{, d2, and d3, we obtain an enhanced image 5.

Multiscale Histogram Equalization

Histogram equalization of transform-space images provides a global method to accomplish multiresolution enhancement.

Traditional histogram equalization was applied to each subband of coefficients in the transform space (excluding the DC component) to obtain a globally enhanced mammogram.

Multiscale Adaptive Gain

In this approach, we suppress pixel values of very small amplitude, and enhance only those pixels larger than a certain threshold T within each level of the transform space. We design the following function to accomplish this nonlinear operation [17]:


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