Adaptive multistage image transform coding is discussed, and an optimal method is introduced for bit allocation. The optimality is in the sense of minimizing the mean square reconstruction error with a given total number of bits and a given number of stages. The statistics of the coefficients in different stages and marginal analysis are used to optimize the division of the total number of bits among the stages. Experimental results indicate that, with two stages, more than 14% improvement for one class and more than 11% improvement for multiclasses is achieved in mean square reconstruction error over one-stage image transform coding. Higher improvements are achieved with three stages. The reconstructed images with multistage coding are subjectively much more preferable than the reconstructed images with one-stage coding.
Blockwise transform image enhancement techniques are discussed. It is shown that the best transforms for transform image coding, namely, the scrambled real discrete Fourier transform, the discrete cosine transform and the discrete cosine-ITT transform, are also the best for image enhancement. Three techniques of enhancement discussed in detail are alpha-rooting, modified unsharp masking, and filtering motivated by the human visual system response (RVS). With proper modifications, it is observed that unsharp masking and HVS-motivated filtering without nonlinearities are basically equivalent. Block effects are completely removed by using an overlap-save technique in addition to the best transform.
Many techniques have been proposed for edge detection involving transforms, such as the method of Shanmugam et al.1 and the gradient method of Marr and Hildreth.2 It can be easily shown that such methods are some kind of bandpass filtering. Because of the existence of different kind of edges and different amount of noise in a real image, no unique filter can be optimal. We discuss how to use some novel real fast transforms for edge detection through bandpass filtering. These are discrete cosine transform (DCT), real discrete Fourier transform (RDFT), scrambled real discrete Fourier transform (SRDFT), and discrete cosine-III transform (DC3T). These transforms also show little block effects, compared to the discrete Fourier transform. They can also be used for interpolation to increase the resolution of edge location and decrease the effect of inherent noise in the real image. For both bandpass filtering and interpolation we applied transforms blockwise to decrease computational complexity to achieve parallel implementation.
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