Exact histogram specification

Abstract

While in the continuous case, statistical models of histogram equalization/specification would yield exact results, their discrete counterparts fail. This is due to the fact that the cumulative distribution functions one deals with are not exactly invertible. Otherwise stated, exact histogram specification for discrete images is an ill-posed problem. Invertible cumulative distribution functions are obtained by translating the problem in a K-dimensional space and further inducing a strict ordering among image pixels. The proposed ordering refines the natural one. Experimental results and statistical models of the induced ordering are presented and several applications are discussed: image enhancement, normalization, watermarking, etc.

Exact global histogram specification optimized for structural similarity

“…A "minor" advantage of the methods based on strict ordering over the proposed method is that they are "almost" completely reversible [13] (or [1]): Suppose that an EHS based on strict ordering is applied to an image. Assuming that you recorded the histogram of the original image before performing EHS, you can perform the same EHS again, this time with the recorded original histogram as the target, to get back the original image (except for the pixels that failed strict ordering; hence "almost" is used above).…”

“…That is because the quality metric we optimized for (SSIM) works for grayscale images only. However, as suggested in [1], one can apply an EHS to the luminance channel of a color image (I, for example, in HSI color space). In this case, our EHS method can be used to better maintain the visual fidelity of the luminance channel, hence improving the overall quality of the color image.…”

“…Continue by assigning the next 1 h pixels a new intensity of 1, and so on until all pixels are assigned their new intensities.…”

“…The output images of the two methods are given in Figure 4. In [2], it is shown that Coltuc's method [1] requires about 10% more CPU time and the quality of its outputs is a bit lower (i.e., not visible in some cases), hence we do not repeat Coltuc results for these images. That is while the improvement in the visual quality of the output is visible in all of our experiments (at least 5.5% higher -19 -SSIM index; see bottom row of Figure 3).…”

Fast wavelet-based pansharpening of multi-spectral images

“…The intensity range of the PAN image is matched to the intensity range of the I channel of the MS image prior to the wavelet decomposition. The intensity matching can be either a simple linear transformation or a nonlinear exact histogram matching, as described in [13]. The pansharpened decomposition is finally recomposed, producing the final pansharpened image (see Fig.…”