Residual Network Naïve solution • If extra layers are an identity mapping, then training errors can not increase 67
Residual Modelling: Basic idea in image processing • Goal: estimate update between an original image and a changed image Preserving base information Some residual Network can treat perturbation 68
Residual Network • Plain block • Difficult to make identity mapping because of multiple non-linear layers 69
Residual Network • Residual block • If identity were optimal, easy to set weights as 0 • If optimal mapping is closer to identity, easier to find small fluctuations Appropriate for treating perturbation as keeping a base information 70
Residual Network: Deeper is better • Deeper ResNets have lower training error 71
Residual Network: Deeper is better 72
CNNs, 2017: DenseNet Densely Connected Convolutional Networks, CVPR 2017 Gao Huang, Zhuang Liu, Laurens van der Maaten, Kilian Q. Weinberger Recently proposed, better performance/parameter ratio 73
Image-to-Image 74
Graphics: Multiresolution 75
Image-to-image • So far we mapped an image image to a number or label • In graphics, output often is “richer”: • An image • A volume • A 3D mesh • … • Note: “ image ” just placeholder name here for any Eulerian data • Architectures • Fully convolutional • Encoder-Decoder • Skip connections 76
Fully-convolutional Neural Networks FCNN 77
Fully-convolutional Neural Networks FCNN 78
Fully-convolutional Neural Networks FCNN 79
Fully-convolutional Neural Networks FCNN 80
Fully-convolutional Neural Networks FCNN Flexible - works with varying input sizes 81
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