Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers—8× deeper than VGG nets [40] but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions1, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

/pdf/deep-residual-learning-for-image-recognition-b75jg61qrq.pdf

Deep Residual Learning for Image Recognition

In this work we investigate the effect of the convolutional network depth on its accuracy in the large-scale image recognition setting. Our main contribution is a thorough evaluation of networks of increasing depth using an architecture with very small (3x3) convolution filters, which shows that a significant improvement on the prior-art configurations can be achieved by pushing the depth to 16-19 weight layers. These findings were the basis of our ImageNet Challenge 2014 submission, where our team secured the first and the second places in the localisation and classification tracks respectively. We also show that our representations generalise well to other datasets, where they achieve state-of-the-art results. We have made our two best-performing ConvNet models publicly available to facilitate further research on the use of deep visual representations in computer vision.

Very Deep Convolutional Networks for Large-Scale Image Recognition

There is large consent that successful training of deep networks requires many thousand annotated training samples. In this paper, we present a network and training strategy that relies on the strong use of data augmentation to use the available annotated samples more efficiently. The architecture consists of a contracting path to capture context and a symmetric expanding path that enables precise localization. We show that such a network can be trained end-to-end from very few images and outperforms the prior best method (a sliding-window convolutional network) on the ISBI challenge for segmentation of neuronal structures in electron microscopic stacks. Using the same network trained on transmitted light microscopy images (phase contrast and DIC) we won the ISBI cell tracking challenge 2015 in these categories by a large margin. Moreover, the network is fast. Segmentation of a 512x512 image takes less than a second on a recent GPU. The full implementation (based on Caffe) and the trained networks are available at http://lmb.informatik.uni-freiburg.de/people/ronneber/u-net .

/pdf/u-net-convolutional-networks-for-biomedical-image-2xoyjzggxv.pdf

U-Net: Convolutional Networks for Biomedical Image Segmentation

Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers---8x deeper than VGG nets but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. 
The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

In this paper, we propose a method, called GridFace, to reduce facial geometric variations and improve the recognition performance. Our method rectifies the face by local homography transformations, which are estimated by a face rectification network. To encourage the image generation with canonical views, we apply a regularization based on the natural face distribution. We learn the rectification network and recognition network in an end-to-end manner. Extensive experiments show our method greatly reduces geometric variations, and gains significant improvements in unconstrained face recognition scenarios.

/pdf/gridface-face-rectification-via-learning-local-homography-1fyegmmjmt.pdf

GridFace: Face Rectification via Learning Local Homography Transformations

Some implementations provide techniques and arrangements to address intrapersonal variations encountered during facial recognition. For example, some implementations employ an identity data set having a plurality of images representing different intrapersonal settings. A predictive model may associate one or more input images with one or more images in the identity data set. Some implementations may use an appearance-prediction approach to compare two images by predicting an appearance of at least one of the images under an intrapersonal setting of the other image. Further, some implementations may utilize a likelihood-prediction approach for comparing images that generates a classifier for an input image based on an association of an input image with the identity data set.

Association and prediction in facial recognition

The Laplace-Beltrami operator (LBO) is a fundamental object associated to Riemannian manifolds, which encodes all intrinsic geometry of the manifolds and has many desirable properties. Recently, we proposed a novel numerical method, Point Integral method (PIM), to discretize the Laplace-Beltrami operator on point clouds \cite{LSS}. In this paper, we analyze the convergence of Point Integral method (PIM) for Poisson equation with Neumann boundary condition on submanifolds isometrically embedded in Euclidean spaces.

Convergence of the Point Integral method for Poisson equation on point cloud

We present an image editing tool called Content-Aware Rotation. Casually shot photos can appear tilted, and are often corrected by rotation and cropping. This trivial solution may remove desired content and hurt image integrity. Instead of doing rigid rotation, we propose a warping method that creates the perception of rotation and avoids cropping. Human vision studies suggest that the perception of rotation is mainly due to horizontal/vertical lines. We design an optimization-based method that preserves the rotation of horizontal/vertical lines, maintains the completeness of the image content, and reduces the warping distortion. An efficient algorithm is developed to address the challenging optimization. We demonstrate our content-aware rotation method on a variety of practical cases.

Content-Aware Rotation

In many real-world applications, data appear to be sampled around 1-dimensional filamentary structures that can be seen as topological metric graphs. In this paper, we address the metric reconstruction problem of such filamentary structures from data sampled around them. We prove that they can be approximated with respect to the Gromov---Hausdorff distance by well-chosen Reeb graphs (and some of their variants) and provide an efficient and easy-to-implement algorithm to compute such approximations in almost linear time. We illustrate the performance of our algorithm on a few datasets.

Jian Sun

Papers

GridFace: Face Rectification via Learning Local Homography Transformations

Association and prediction in facial recognition

Convergence of the Point Integral method for Poisson equation on point cloud

Content-Aware Rotation

Gromov---Hausdorff Approximation of Filamentary Structures Using Reeb-Type Graphs