Page - 119 - in Joint Austrian Computer Vision and Robotics Workshop 2020

Figure 1. Comparison of weighting methods. A sample image (left) and weight maps for Median Frequency Bal- ancing (left middle), Boundary Proximity (right middle) andGradientRatio (right). Figure 2. Examples of an overexposed bright region (left) andanunderexposeddark region (right). LMSE LBCE Default 1.189×10−2 1.145×10−2 MFB 1.284×10−2 1.114×10−2 BoundaryProximity 1.217×10−2 1.126×10−2 GradientRatio 1.296×10−2 1.108×10−2 MFB+ GradientRatio 1.282×10−2 1.106×10−2 Table 1. Comparison of network performance after train- ing with Mean Squared ErrorLMSE and Binary Cross- EntropyLBCEmeasuredby1−Jaccard index. 4.2.GradientLoss We expand on the idea of using discrete gradients in loss functions and introduce the Gradient Loss. This loss is inspired by theH1 Sobolev seminorm |f|H1 := ‖∇f‖L2. Instead of optimizing the plain value of the segmentation mask we optimize its gra- dient: L∇(p,t) :=LMSE(∇σp,∇σt) (5) In our tests we observe that neural networks trained with this loss produce masks with cleaner constant regions. We believe it allows them to learn that seg- mentation masks should be largely constant, i.e. for mostareas∇σp shouldbezero. It isnot advisable to usetheGradientLossonitsownsinceit isbasedonly on a seminorm. Depending on how the convolution treats missing values on the boundaries there might holdL∇(p+ c,t) =L∇(p,t) for constant values c 1−Jaccard index LDSC 9.237×10−3 LBCE 1.145×10−2 LMSE 1.189×10−2 LDSC+LBCE 1.045×10−2 LDSC+LMSE 9.633×10−3 LBCE+L∇ 1.082×10−2 LMSE+L∇ 1.224×10−2 LDSC+LBCE+L∇ 1.027×10−2 LDSC+LMSE+L∇ 9.118×10−3 Previous solution 2.640×10−2 Table2.Networkperformanceafter trainingwithcompos- ite loss functionsmeasure by1−Jaccard index. (invariance to constant shifts). If the Gradient Loss iscombinedwithMeanSquaredErrorweessentially obtainadiscreteversionof theH1Sobolevnorm. 4.3.CompositeLossResults It is common practice to combine the Dice Loss with a pixelwise loss [8] which results in segmenta- tionmapswithsharperboundaries. Thecombination of multiple loss functions is achieved by simple ad- dition of the individual losses. Addition of the Dice Loss to the pixelwise losses uniformly results in a performance increase (see Table 2) due to its close relation to the Jaccard index. In these tests Mean Squared Error surpasses Binary Cross-Entropy by a significantmarginwhile the incorporationofweight- ing schemes worsened results. The further addition of the Gradient Loss leads to mixed, but generally positive results. Although the effects on the combi- nation of Dice Loss and Binary Cross-Entropy are minor, we achieve overall best results with the com- binationof the three lossesDiceLoss,MeanSquared Error and Gradient Loss. The score outperforms the previous best result which was achieved with plain Dice Loss. Compared to a previous implementation usedby theCarCutter service the segmentationerror is reducedby65%. 4.4.Postprocessing The proposed weighting schemes and loss func- tions can only work if over- or underexposed re- gions are not completely devoid of texture. Other- wise a neural network may only learn to predict a pixel’s probability to belong to the foreground class which inevitably causes non-sharp transition in the predicted masks. An alternate approach is the use of acustompostprocessingprocedure. 119