Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation

Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies. Morphable Models and their variants, despite their linear formulation, have been widely used for shape representation, while most of the recently proposed nonlinear approaches resort to intermediate representations, such as 3D voxel grids or 2D views. In this work, we introduce a novel graph convolutional operator, acting directly on the 3D mesh, that explicitly models the inductive bias of the fixed underlying graph. This is achieved by enforcing consistent local orderings of the vertices of the graph, through the spiral operator, thus breaking the permutation invariance property that is adopted by all the prior work on Graph Neural Networks. Our operator comes by construction with desirable properties (anisotropic, topology-aware, lightweight, easy-to-optimise), and by using it as a building block for traditional deep generative architectures, we demonstrate state-of-the-art results on a variety of 3D shape datasets compared to the linear Morphable Model and other graph convolutional operators.Comment: to appear at ICCV 201

BLADE: Filter Learning for General Purpose Computational Photography

The Rapid and Accurate Image Super Resolution (RAISR) method of Romano, Isidoro, and Milanfar is a computationally efficient image upscaling method using a trained set of filters. We describe a generalization of RAISR, which we name Best Linear Adaptive Enhancement (BLADE). This approach is a trainable edge-adaptive filtering framework that is general, simple, computationally efficient, and useful for a wide range of problems in computational photography. We show applications to operations which may appear in a camera pipeline including denoising, demosaicing, and stylization

Dynamically reconfigurable management of energy, performance, and accuracy applied to digital signal, image, and video Processing Applications

There is strong interest in the development of dynamically reconfigurable systems that can meet real-time constraints in energy/power-performance-accuracy (EPA/PPA). In this dissertation, I introduce a framework for implementing dynamically reconfigurable digital signal, image, and video processing systems. The basic idea is to first generate a collection of Pareto-optimal realizations in the EPA/PPA space. Dynamic EPA/PPA management is then achieved by selecting the Pareto-optimal implementations that can meet the real-time constraints. The systems are then demonstrated using Dynamic Partial Reconfiguration (DPR) and dynamic frequency control on FPGAs. The framework is demonstrated on: i) a dynamic pixel processor, ii) a dynamically reconfigurable 1-D digital filtering architecture, and iii) a dynamically reconfigurable 2-D separable digital filtering system. Efficient implementations of the pixel processor are based on the use of look-up tables and local-multiplexes to minimize FPGA resources. For the pixel-processor, different realizations are generated based on the number of input bits, the number of cores, the number of output bits, and the frequency of operation. For each parameters combination, there is a different pixel-processor realization. Pareto-optimal realizations are selected based on measurements of energy per frame, PSNR accuracy, and performance in terms of frames per second. Dynamic EPA/PPA management is demonstrated for a sequential list of real-time constraints by selecting optimal realizations and implementing using DPR and dynamic frequency control. Efficient FPGA implementations for the 1-D and 2-D FIR filters are based on the use a distributed arithmetic technique. Different realizations are generated by varying the number of coefficients, coefficient bitwidth, and output bitwidth. Pareto-optimal realizations are selected in the EPA space. Dynamic EPA management is demonstrated on the application of real-time EPA constraints on a digital video. The results suggest that the general framework can be applied to a variety of digital signal, image, and video processing systems. It is based on the use of offline-processing that is used to determine the Pareto-optimal realizations. Real-time constraints are met by selecting Pareto-optimal realizations pre-loaded in memory that are then implemented efficiently using DPR and/or dynamic frequency control

ARKCoS: Artifact-Suppressed Accelerated Radial Kernel Convolution on the Sphere

We describe a hybrid Fourier/direct space convolution algorithm for compact radial (azimuthally symmetric) kernels on the sphere. For high resolution maps covering a large fraction of the sky, our implementation takes advantage of the inexpensive massive parallelism afforded by consumer graphics processing units (GPUs). Applications involve modeling of instrumental beam shapes in terms of compact kernels, computation of fine-scale wavelet transformations, and optimal filtering for the detection of point sources. Our algorithm works for any pixelization where pixels are grouped into isolatitude rings. Even for kernels that are not bandwidth limited, ringing features are completely absent on an ECP grid. We demonstrate that they can be highly suppressed on the popular HEALPix pixelization, for which we develop a freely available implementation of the algorithm. As an example application, we show that running on a high-end consumer graphics card our method speeds up beam convolution for simulations of a characteristic Planck high frequency instrument channel by two orders of magnitude compared to the commonly used HEALPix implementation on one CPU core while maintaining at typical a fractional RMS accuracy of about 1 part in 10^5.Comment: 10 pages, 6 figures. Submitted to Astronomy and Astrophysics. Replaced to match published version. Code can be downloaded at https://github.com/elsner/arkco

Are Compact Hyperbolic Models Observationally Ruled Out?

We revisit the observational constraints on compact(closed) hyperbolic(CH) models from cosmic microwave background(CMB). We carry out Bayesian analyses for CH models with volume comparable to the cube of the present curvature radius using the COBE-DMR data and show that a slight suppression in the large-angle temperature correlations owing to the non-trivial topology explains rather naturally the observed anomalously low quadrupole which is incompatible with the prediction of the standard infinite Friedmann-Robertson-Walker models. While most of positions and orientations are ruled out, the likelihoods of CH models are found to be much better than those of infinite counterparts for some specific positions and orientations of the observer, leading to less stringent constraints on the volume of the manifolds. Even if the spatial geometry is nearly flat as $\Omega_{tot}=0.9-0.95$, suppression of the angular power on large angular scales is still prominent for CH models with volume much less than the cube of the present curvature radius if the cosmological constant is dominant at present.Comment: 25 pages, 16 EPS figures Version accepted for publication in PT