To better preserve features, 3D anisotropic diffusionfilters are chosen (at the expense of computation time). Thus, Gaussian filters (discretized as binomial filters) are used as simple techniques. Noise reduction in perfusion data is performed similarly to noise reduction in static image data. The values highlighted in bold indicate the highest accuracy obtained for the particular data set.īernhard Preim, Charl Botha, in Visual Computing for Medicine (Second Edition), 2014 16.3.4 Noise Reduction Similarly, the results can be analyzed for the other two data sets. In the detailed analysis, Table 15.10A-C gives the statistics for three data sets: leukemia, breast cancer, and ovarian cancer, respectively.įrom the obtained results, it is clear that when t-test is used as a FS method, a set of 14 features with γ = 2 5, C = 2 3 values are sufficient enough to achieve 99.69% training accuracy and 100.00% testing accuracy for the leukemia data set.
The table gives the values of statistics such as the number of features (which obtained better accuracy for the respective FS method) and accuracy obtained for the training and testing phases. The shifting effect is not avoided simply by employing a different central-seeking statistic to perform the averaging.įrom Table 15.10, it is inferred that the number of features required corresponds to the optimal value of γ and C with their training and testing accuracy. All such filters have similar shifting effects because they all incorporate a measure of signal averaging. The results for Gaussian filters do not differ substantially from those for mean filters but have to be obtained by integration, taking account of the Gaussian weighting function ( Davies, 1991b). These considerations complete the entries in Table 3.2. The results cannot be obtained by intuitive or simple geometric or intuitive arguments, and here we merely quote the shift for the mean filter as being 1/8 κa 2.
In the case of a smoothly varying slant edge, the result for the mean filter has to be calculated by integrating over the area of the neighborhood. Hence, it also gives a shift of 1/6 κa 2 for a curved step edge. At that point the mean filter must give the same result, since all three statistics coincide for a symmetrical distribution. It is identical to that for the median and mode filters, and it follows because of the symmetry of the local intensity distribution at the point where the filter switches from a left-hand to a right-hand decision. The situation for a curved step edge can again be understood by appealing to Fig. Again, we will ignore the effects of noise because we are considering the intrinsic rather than the noise-induced behavior of the filters. We again consider the two paradigm cases-step edges and slant edges with circular boundaries.
As in the cases of median and mode filters, straight edges with symmetrical profiles cannot be shifted by mean and Gaussian filters, because of symmetry. In this section, we consider the shifts produced by mean and Gaussian filters in continuous images. DAVIES, in Machine Vision (Third Edition), 2005 3.11 Shifts Introduced by Mean and Gaussian Filters