Validation of the Average Image

Questions of significance and reproducibility of features have been addressed above in this chapter (section 4.2). The problem with such treatments is that they must be based on assumptions regarding the statistical distribution of the noise. In the following we will discuss a technique that requires no such assumptions.

The question of significance of features in the average image can be addressed by a method of multiple comparison that makes no assumptions regarding the statistics: the rank sum method (Hanicke, 1981; Hanicke et al., 1984). Given a set of N images, each represented by J pixels:

The nonparametric statistical test is designed as follows: each pixel pij of the ith image is ranked according to its value among the entire set of pixels {pj j = 1..., J}: the pixel with the lowest value is assigned rank 1, the second lowest, rank 2, and so forth. Finally, the pixel with the largest value receives rank J. In the case of value ties, all pixels within the equal-value group are assigned an average rank. In the end, the image is represented by a set of rank samples {ri1, ri2,..., riJ}, which is a permutation of the set of ordered integers {1,2,..., J} (except for those rank samples that result from ties). After forming such rank representations for each image, we form a rank sum for each pixel:

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