3.2.1 Anisotropic Di usion Filtering[6]
Perona-Malik Anisotropic Di usion is a nonlinear smoothing lter which uses a variable conductance term, that controls the contrast of the edges that in uence the di usion.This ltering method is mathematically formulated as a di usion process and encourages intraregion smoothing in preference to smoothing across boundaries.The advantage of this ltering method is that it can smooth small discontinuities caused by background noise using gradient information and can preserve large intensity variations caused by edges. Here a noise reduction method post- process based on anisotropic di usion is used. The anisotropic di usion per- forms a piecewise smoothing of the original signal. The propagation of information between discontinuities results in regions of constant intensity or linear variations of low frequency.This method supports 3-D and multi-echo MRI, incorporating higher spatial and spectral dimensions. It overcomes the major drawbacks of conventional lter methods, namely the blurring of object boundaries and the suppression of ne structural details.
3.2.2 Total Variation Minimization Scheme[7]
Anisotropic di usion and its variants totally depend on gradient values to decide the type of di usion and amount of smoothing: when the gradient is high, it applies less isotropic di usion and thus smoothes less across edges; when the gradient is low, it smoothes more isotropically and thus smooth more. Thus it works only if high gradients happens on edges only. However, for images with spatially unevenly distributed noise and artifacts, the noise is so high in some regions, and the artifacts are so pronounced in some areas that high gradient values could happen in all three places: edges, arti...
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...]. Determining the parameters in Con- trast Limited Adaptive Histogram Equalization are discussed in[26]. Block size and clip limit are used to control the quality of results of CLAHE.The value at which the histogram is clipped, called clip limit depends on the normalization of the histogram and thereby on the size of the neighbourhood region.CLAHE limits the noise enhancement by establishing a maximum value or clip limit, a bin can hold in the histogram of an image tile. This method enhances images with very low contrast.
From the above statistics,it is observed that the method with low Absolute mean brightness error(AMBE) can preserve average brightness and the method with less RMS contrast shows that there is no more deviation from mean i.e. mean is preserved.Eventhough AHE has less AMBE,it introduces some blocky e ects.This drawback is somewhat reduced by CLAHE.