In this paper, we show how a 3D Morphable Model (i.e. a statistical model of the 3D shape of a class of objects such as faces) can be used to spatially transform input data as a module (a 3DMM-STN) within a convolutional neural network. This is an extension of the original spatial transformer network in that we are able to interpret and normalise 3D pose changes and self-occlusions. The trained localisation part of the network is independently useful since it learns to fit a 3D morphable model to a single image. We show that the localiser can be trained using only simple geometric loss functions on a relatively small dataset yet is able to perform robust normalisation on highly uncontrolled images including occlusion, self-occlusion and large pose changes.
The original STN @cite_14 aimed to combine these two processes into a single network that is trainable end to end. The localiser network estimated a 2D affine transformation that was applied to the regular output grid meaning the network could only learn a fairly restricted space of transformations. Jaderberg al @cite_14 also proposed the concept of a 3D transformer, which takes 3D voxel data as input, applies 3D rotation and translation, and outputs a 2D projection of the transformed data. Working with 3D (volumetric data) removes the need to model occlusion or camera projection parameters. In contrast, we work with regular 2D input and output images but transform them via a 3D model.
@cite_14
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In this paper, we show how a 3D Morphable Model (i.e. a statistical model of the 3D shape of a class of objects such as faces) can be used to spatially transform input data as a module (a 3DMM-STN) within a convolutional neural network. This is an extension of the original spatial transformer network in that we are able to interpret and normalise 3D pose changes and self-occlusions. The trained localisation part of the network is independently useful since it learns to fit a 3D morphable model to a single image. We show that the localiser can be trained using only simple geometric loss functions on a relatively small dataset yet is able to perform robust normalisation on highly uncontrolled images including occlusion, self-occlusion and large pose changes. Convolutional neural networks (CNNs) are inherently equivariant to translation. Efforts to embed other forms of equivariance have concentrated solely on rotation. We expand the notion of equivariance in CNNs through the Polar Transformer Network (PTN). PTN combines ideas from the Spatial Transformer Network (STN) and canonical coordinate representations. The result is a network invariant to translation and equivariant to both rotation and scale. PTN is trained end-to-end and composed of three distinct stages: a polar origin predictor, the newly introduced polar transformer module and a classifier. PTN achieves state-of-the-art on rotated MNIST and the newly introduced SIM2MNIST dataset, an MNIST variation obtained by adding clutter and perturbing digits with translation, rotation and scaling. The ideas of PTN are extensible to 3D which we demonstrate through the Cylindrical Transformer Network We propose a novel approach to 3D human pose estimation from a single depth map. Recently, convolutional neural network (CNN) has become a powerful paradigm in computer vision. Many of computer vision tasks have benefited from CNNs, however, the conventional approach to directly regress 3D body joint locations from an image does not yield a noticeably improved performance. In contrast, we formulate the problem as estimating per-voxel likelihood of key body joints from a 3D occupancy grid. We argue that learning a mapping from volumetric input to volumetric output with 3D convolution consistently improves the accuracy when compared to learning a regression from depth map to 3D joint coordinates. We propose a two-stage approach to reduce the computational overhead caused by volumetric representation and 3D convolution: Holistic 2D prediction and Local 3D prediction. In the first stage, Planimetric Network (P-Net) estimates per-pixel likelihood for each body joint in the holistic 2D space. In the second stage, Volumetric Network (V-Net) estimates the per-voxel likelihood of each body joints in the local 3D space around the 2D estimations of the first stage, effectively reducing the computational cost. Our model outperforms existing methods by a large margin in publicly available datasets. We present a transformation-grounded image generation network for novel 3D view synthesis from a single image. Our approach first explicitly infers the parts of the geometry visible both in the input and novel views and then casts the remaining synthesis problem as image completion. Specifically, we both predict a flow to move the pixels from the input to the novel view along with a novel visibility map that helps deal with occulsion disocculsion. Next, conditioned on those intermediate results, we hallucinate (infer) parts of the object invisible in the input image. In addition to the new network structure, training with a combination of adversarial and perceptual loss results in a reduction in common artifacts of novel view synthesis such as distortions and holes, while successfully generating high frequency details and preserving visual aspects of the input image. We evaluate our approach on a wide range of synthetic and real examples. Both qualitative and quantitative results show our method achieves significantly better results compared to existing methods.