15,972 research outputs found
Perspective Plane Program Induction from a Single Image
We study the inverse graphics problem of inferring a holistic representation
for natural images. Given an input image, our goal is to induce a
neuro-symbolic, program-like representation that jointly models camera poses,
object locations, and global scene structures. Such high-level, holistic scene
representations further facilitate low-level image manipulation tasks such as
inpainting. We formulate this problem as jointly finding the camera pose and
scene structure that best describe the input image. The benefits of such joint
inference are two-fold: scene regularity serves as a new cue for perspective
correction, and in turn, correct perspective correction leads to a simplified
scene structure, similar to how the correct shape leads to the most regular
texture in shape from texture. Our proposed framework, Perspective Plane
Program Induction (P3I), combines search-based and gradient-based algorithms to
efficiently solve the problem. P3I outperforms a set of baselines on a
collection of Internet images, across tasks including camera pose estimation,
global structure inference, and down-stream image manipulation tasks.Comment: CVPR 2020. First two authors contributed equally. Project page:
http://p3i.csail.mit.edu
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemporary
signal processing, where the goal is to reconstruct an unknown signal from
partial indirect, and possibly noisy, measurements of it. A now standard method
for recovering the unknown signal is to solve a convex optimization problem
that enforces some prior knowledge about its structure. This has proved
efficient in many problems routinely encountered in imaging sciences,
statistics and machine learning. This chapter delivers a review of recent
advances in the field where the regularization prior promotes solutions
conforming to some notion of simplicity/low-complexity. These priors encompass
as popular examples sparsity and group sparsity (to capture the compressibility
of natural signals and images), total variation and analysis sparsity (to
promote piecewise regularity), and low-rank (as natural extension of sparsity
to matrix-valued data). Our aim is to provide a unified treatment of all these
regularizations under a single umbrella, namely the theory of partial
smoothness. This framework is very general and accommodates all low-complexity
regularizers just mentioned, as well as many others. Partial smoothness turns
out to be the canonical way to encode low-dimensional models that can be linear
spaces or more general smooth manifolds. This review is intended to serve as a
one stop shop toward the understanding of the theoretical properties of the
so-regularized solutions. It covers a large spectrum including: (i) recovery
guarantees and stability to noise, both in terms of -stability and
model (manifold) identification; (ii) sensitivity analysis to perturbations of
the parameters involved (in particular the observations), with applications to
unbiased risk estimation ; (iii) convergence properties of the forward-backward
proximal splitting scheme, that is particularly well suited to solve the
corresponding large-scale regularized optimization problem
An MDL framework for sparse coding and dictionary learning
The power of sparse signal modeling with learned over-complete dictionaries
has been demonstrated in a variety of applications and fields, from signal
processing to statistical inference and machine learning. However, the
statistical properties of these models, such as under-fitting or over-fitting
given sets of data, are still not well characterized in the literature. As a
result, the success of sparse modeling depends on hand-tuning critical
parameters for each data and application. This work aims at addressing this by
providing a practical and objective characterization of sparse models by means
of the Minimum Description Length (MDL) principle -- a well established
information-theoretic approach to model selection in statistical inference. The
resulting framework derives a family of efficient sparse coding and dictionary
learning algorithms which, by virtue of the MDL principle, are completely
parameter free. Furthermore, such framework allows to incorporate additional
prior information to existing models, such as Markovian dependencies, or to
define completely new problem formulations, including in the matrix analysis
area, in a natural way. These virtues will be demonstrated with parameter-free
algorithms for the classic image denoising and classification problems, and for
low-rank matrix recovery in video applications
Diffeomorphic density registration
In this book chapter we study the Riemannian Geometry of the density
registration problem: Given two densities (not necessarily probability
densities) defined on a smooth finite dimensional manifold find a
diffeomorphism which transforms one to the other. This problem is motivated by
the medical imaging application of tracking organ motion due to respiration in
Thoracic CT imaging where the fundamental physical property of conservation of
mass naturally leads to modeling CT attenuation as a density. We will study the
intimate link between the Riemannian metrics on the space of diffeomorphisms
and those on the space of densities. We finally develop novel computationally
efficient algorithms and demonstrate there applicability for registering RCCT
thoracic imaging.Comment: 23 pages, 6 Figures, Chapter for a Book on Medical Image Analysi
Semantic Visual Localization
Robust visual localization under a wide range of viewing conditions is a
fundamental problem in computer vision. Handling the difficult cases of this
problem is not only very challenging but also of high practical relevance,
e.g., in the context of life-long localization for augmented reality or
autonomous robots. In this paper, we propose a novel approach based on a joint
3D geometric and semantic understanding of the world, enabling it to succeed
under conditions where previous approaches failed. Our method leverages a novel
generative model for descriptor learning, trained on semantic scene completion
as an auxiliary task. The resulting 3D descriptors are robust to missing
observations by encoding high-level 3D geometric and semantic information.
Experiments on several challenging large-scale localization datasets
demonstrate reliable localization under extreme viewpoint, illumination, and
geometry changes
Structured Sparsity: Discrete and Convex approaches
Compressive sensing (CS) exploits sparsity to recover sparse or compressible
signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity
is also used to enhance interpretability in machine learning and statistics
applications: While the ambient dimension is vast in modern data analysis
problems, the relevant information therein typically resides in a much lower
dimensional space. However, many solutions proposed nowadays do not leverage
the true underlying structure. Recent results in CS extend the simple sparsity
idea to more sophisticated {\em structured} sparsity models, which describe the
interdependency between the nonzero components of a signal, allowing to
increase the interpretability of the results and lead to better recovery
performance. In order to better understand the impact of structured sparsity,
in this chapter we analyze the connections between the discrete models and
their convex relaxations, highlighting their relative advantages. We start with
the general group sparse model and then elaborate on two important special
cases: the dispersive and the hierarchical models. For each, we present the
models in their discrete nature, discuss how to solve the ensuing discrete
problems and then describe convex relaxations. We also consider more general
structures as defined by set functions and present their convex proxies.
Further, we discuss efficient optimization solutions for structured sparsity
problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure
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