Header logo is


2013


Puppet Flow
Puppet Flow

Zuffi, S., Black, M. J.

(7), Max Planck Institute for Intelligent Systems, October 2013 (techreport)

Abstract
We introduce Puppet Flow (PF), a layered model describing the optical flow of a person in a video sequence. We consider video frames composed by two layers: a foreground layer corresponding to a person, and background. We model the background as an affine flow field. The foreground layer, being a moving person, requires reasoning about the articulated nature of the human body. We thus represent the foreground layer with the Deformable Structures model (DS), a parametrized 2D part-based human body representation. We call the motion field defined through articulated motion and deformation of the DS model, a Puppet Flow. By exploiting the DS representation, Puppet Flow is a parametrized optical flow field, where parameters are the person's pose, gender and body shape.

ps

pdf Project Page Project Page [BibTex]

2013


pdf Project Page Project Page [BibTex]


Statistics on Manifolds with Applications to Modeling Shape Deformations
Statistics on Manifolds with Applications to Modeling Shape Deformations

Freifeld, O.

Brown University, August 2013 (phdthesis)

Abstract
Statistical models of non-rigid deformable shape have wide application in many fi elds, including computer vision, computer graphics, and biometry. We show that shape deformations are well represented through nonlinear manifolds that are also matrix Lie groups. These pattern-theoretic representations lead to several advantages over other alternatives, including a principled measure of shape dissimilarity and a natural way to compose deformations. Moreover, they enable building models using statistics on manifolds. Consequently, such models are superior to those based on Euclidean representations. We demonstrate this by modeling 2D and 3D human body shape. Shape deformations are only one example of manifold-valued data. More generally, in many computer-vision and machine-learning problems, nonlinear manifold representations arise naturally and provide a powerful alternative to Euclidean representations. Statistics is traditionally concerned with data in a Euclidean space, relying on the linear structure and the distances associated with such a space; this renders it inappropriate for nonlinear spaces. Statistics can, however, be generalized to nonlinear manifolds. Moreover, by respecting the underlying geometry, the statistical models result in not only more e ffective analysis but also consistent synthesis. We go beyond previous work on statistics on manifolds by showing how, even on these curved spaces, problems related to modeling a class from scarce data can be dealt with by leveraging information from related classes residing in di fferent regions of the space. We show the usefulness of our approach with 3D shape deformations. To summarize our main contributions: 1) We de fine a new 2D articulated model -- more expressive than traditional ones -- of deformable human shape that factors body-shape, pose, and camera variations. Its high realism is obtained from training data generated from a detailed 3D model. 2) We defi ne a new manifold-based representation of 3D shape deformations that yields statistical deformable-template models that are better than the current state-of-the- art. 3) We generalize a transfer learning idea from Euclidean spaces to Riemannian manifolds. This work demonstrates the value of modeling manifold-valued data and their statistics explicitly on the manifold. Specifi cally, the methods here provide new tools for shape analysis.

ps

pdf Project Page [BibTex]


Learning and Optimization with Submodular Functions
Learning and Optimization with Submodular Functions

Sankaran, B., Ghazvininejad, M., He, X., Kale, D., Cohen, L.

ArXiv, May 2013 (techreport)

Abstract
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it is beneficial to have strong guarantees on the tractable approximate solutions. In order operate under these criterion most optimization problems are cast under the umbrella of convexity or submodularity. In this report we will study design and optimization over a common class of functions called submodular functions. Set functions, and specifically submodular set functions, characterize a wide variety of naturally occurring optimization problems, and the property of submodularity of set functions has deep theoretical consequences with wide ranging applications. Informally, the property of submodularity of set functions concerns the intuitive principle of diminishing returns. This property states that adding an element to a smaller set has more value than adding it to a larger set. Common examples of submodular monotone functions are entropies, concave functions of cardinality, and matroid rank functions; non-monotone examples include graph cuts, network flows, and mutual information. In this paper we will review the formal definition of submodularity; the optimization of submodular functions, both maximization and minimization; and finally discuss some applications in relation to learning and reasoning using submodular functions.

am

arxiv link (url) [BibTex]

arxiv link (url) [BibTex]


A Quantitative Analysis of Current Practices in Optical Flow Estimation and the Principles Behind Them
A Quantitative Analysis of Current Practices in Optical Flow Estimation and the Principles Behind Them

Sun, D., Roth, S., Black, M. J.

(CS-10-03), Brown University, Department of Computer Science, January 2013 (techreport)

ps

pdf [BibTex]

pdf [BibTex]