Shape Synthesis and Analysis by Deformable Models

Matan Sela, Ph.D. Thesis Seminar
Thursday, 8.2.2018, 11:30
Taub 401
Prof. Ron Kimmel

The surface separating the interior of a given object or body from its exterior defines a shape. A key challenge in computer vision is to recover the shape from missing, partial, sparse or noisy observations such as images, depth maps or position sensors. Although in theory, surfaces can be arbitrarily embedded in space, the underlying structure of deformable shapes, such as the human face, is often driven by just a few degrees of freedom. For example, it has been shown that the space of the coarse geometric structure of faces can be well represented in a low dimensional Euclidean space. Similarly, the motion of articulated objects, such as the human body, is controlled by a small set of number of parameters controlling the skeletal structure of connections between limbs and bones. The goal of this research is to analyze and synthesize shapes based on low dimensional, learnable, and axiomatic deformable models. We begin by proposing a novel method for recovering the coarse structure of a face from a single image. We demonstrate that training a convolutional neural network with synthetic images drawn from a statistical deformable model allows robust reconstructions under large pose, lighting and expression variations. For recovering subtle structures, such as wrinkles, we devise a deep deformable model guided by a photometric (axiomatic) image formation model. In this model, the coarse structure is still restricted to a low dimensional deformable model. Next, we relieve this constraint and train an image to image mapping network with samples from the deformable model. Surprisingly, the network was able to reconstruct unique geometries that cannot be represented by the model. Along a similar line of thought, we propose a multi-linear blend skinning framework for constructing a low dimensional deformation model of articulated objects from a few isometries. This model allows to effectively predict a plausible configuration of the shape from a sparse set of constraints, as well as completing and registering the shape to a partial observation. Finally, we define a numerical scheme for computing and optimizing the L1 norm of functions defined over deformable triangulated models. To handle a Steiffel manifold constraint, we propose an iteratively reweighted least squares algorithm with an additional projection step based on the Gershgorin Circle theorem. The framework allows to efficiently optimize L1 regularized objective functions on the surface even under non-convex constraints.

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