Page - 186 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

The segmentation error is evaluated on the reconstructed grayscale images of the LBP pyramid on a range from 0 to 5000 segments. Figure 3 shows the reconstructed images of the LBP pyramid for 200, 500, 1000 and 2000 segments as well as the magnitudes of the 2D Fourier transform. It is well visible that the frequenciesareevenlydistributed. AFourier transformofaLaplacianpyramidshows circular structuresdue to thebandpasseffectof thispyramid, for aGaussianpyramid lowpasseffects are visible in the frequency domain. Since these effects are not visible in the Fourier transforms of theLBPpyramidweconclude that theLBPpyramid doesnothaveabandpassnora lowpasseffect. 3.3. ValidationMethodology For estimating the empirical segmentation error against the ground truth images, the region-based segmentationmeasurementGlobalConsistencyError (GCE)[12] isused. It isa robust techniqueand independent of thenumberof segments ineach image. TheGCEisdefinedas: GCE(S1,S2)= 1 n min (∑ i E(S1,S2,pi), ∑ i E(S2,S1,pi) ) (1) To measure the same local refinement errorEwhen changing the order of the reference image such thatE(S1,S2,pi) = E(S2,S1,pi), we take the minimum of both sums over all pixels in the GCE computation. Inorder todefineE,wefirstdenote thesetdifferenceofAandB asA\B, and |A| the cardinalityof thesetA. LetR(S,pi)be thesetofpixels in thesegmented imageS that correspond to the regionRcontainingpixelspi, then the local refinementerrorE isdefinedas: E(S1,S2,pi)= |R(S1,pi)\R(S2,pi)| |R(S1,pi)| (2) 4. Results The GCE error is evaluated for all 26 test images for the range of 0 to 5000 segments, both for the reconstruction of the original images and of the noisy images. Figure 4 shows the original and the noisy images reconstructed with a different number of segments (compare with Figure 2b showing theground truth). As we can observe in Figure 4b, we expect the noise to introduce additional high frequencies to the original image and hence to result in smaller regions compared to the reconstruction of the original image (Figure 4a) for the same number of segments. For a bigger SNR, this effect should be less visible suchas inFigure4cand4d. Figure 5a shows the GCE evaluation of the reconstructed test images with an increasing number of segments. If one compares the GCE obtained from the original segmentation to the segmentation of the images with uniformly distributed noise (see Figure 5b), we observe that the GCE curves are (a)Uniform noise (b)Gaussiannoise (c) Poissonnoise Figure1: Normalized noisedistributions 186