Or Litany

Non-rigid puzzles

Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non‐rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non‐rigid multi‐part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non‐rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario.

Fully Spectral Partial Shape Matching

We propose an efficient procedure for calculating partial dense intrinsic correspondence between deformable shapes performed entirely in the spectral domain. Our technique relies on the recently introduced partial functional maps formalism and on the joint approximate diagonalization (JAD) of the Laplace‐Beltrami operators previously introduced for matching non‐isometric shapes. We show that a variant of the JAD problem with an appropriately modified coupling term (surprisingly) allows to construct quasi‐harmonic bases localized on the latent corresponding parts. This circumvents the need to explicitly compute the unknown parts by means of the cumbersome alternating minimization used in the previous approaches, and allows performing all the calculations in the spectral domain with constant complexity independent of the number of shape vertices. We provide an extensive evaluation of the proposed technique on standard non‐rigid correspondence benchmarks and show state‐of‐the‐art performance in various settings, including partiality and the presence of topological noise.

Putting the pieces together: regularized multi-part shape matching

Multi-part shape matching is an important class of problems, arising in many fields such as computational archaeology, biology, geometry processing, computer graphics and vision. In this paper, we address the problem of simultaneous matching and segmentation of multiple shapes. We assume to be given a reference shape and multiple parts partially matching the reference. Each of these parts can have additional clutter, have overlap with other parts, or there might be missing parts. We show experimental results of efficient and accurate assembly of fractured synthetic and real objects.

ASIST: Automatic semantically invariant scene transformation

We present ASIST, a technique for transforming point clouds by replacing objects with their semantically equivalent counterparts. Transformations of this kind have applications in virtual reality, repair of fused scans, and robotics. ASIST is based on a unified formulation of semantic labeling and object replacement; both result from minimizing a single objective. We present numerical tools for the efficient solution of this optimization problem. The method is experimentally assessed on new datasets of both synthetic and real point clouds, and is additionally compared to two recent works on object replacement on data from the corresponding papers.

A picture is worth a billion bits: Real-time image reconstruction from dense binary threshold pixels

The pursuit of smaller pixel sizes at ever increasing resolution in digital image sensors is mainly driven by the stringent price and form-factor requirements of sensors and optics in the cellular phone market. Recently, Eric Fossum proposed a novel concept of an image sensor with dense sub-diffraction limit one-bit pixels (jots), which can be considered a digital emulation of silver halide photographic film. This idea has been recently embodied as the EPFL Gigavision camera. A major bottleneck in the design of such sensors is the image reconstruction process, producing a continuous high dynamic range image from oversampled binary measurements. The extreme quantization of the Poisson statistics is incompatible with the assumptions of most standard image processing and enhancement frameworks. The recently proposed maximum-likelihood (ML) approach addresses this difficulty, but suffers from image artefacts and has impractically high computational complexity. In this work, we study a variant of a sensor with binary threshold pixels and propose a reconstruction algorithm combining an ML data fitting term with a sparse synthesis prior. We also show an efficient hardware-friendly real-time approximation of this inverse operator. Promising results are shown on synthetic data as well as on HDR data emulated using multiple exposures of a regular CMOS sensor.

White Matter Fiber Representation Using Continuous Dictionary Learning

With increasingly sophisticated Diffusion Weighted MRI acquisition methods and modeling techniques, very large sets of streamlines (fibers) are presently generated per imaged brain. These reconstructions of white matter architecture, which are important for human brain research and pre-surgical planning, require a large amount of storage and are often unwieldy and difficult to manipulate and analyze. This work proposes a novel continuous parsimonious framework in which signals are sparsely represented in a dictionary with continuous atoms. The significant innovation in our new methodology is the ability to train such continuous dictionaries, unlike previous approaches that either used pre-fixed continuous transforms or training with finite atoms. This leads to an innovative fiber representation method, which uses Continuous Dictionary Learning to sparsely code each fiber with high accuracy. This method is tested on numerous tractograms produced from the Human Connectome Project data and achieves state-of-the-art performances in compression ratio and reconstruction error.