28,510 research outputs found
Second-order Shape Optimization for Geometric Inverse Problems in Vision
We develop a method for optimization in shape spaces, i.e., sets of surfaces
modulo re-parametrization. Unlike previously proposed gradient flows, we
achieve superlinear convergence rates through a subtle approximation of the
shape Hessian, which is generally hard to compute and suffers from a series of
degeneracies. Our analysis highlights the role of mean curvature motion in
comparison with first-order schemes: instead of surface area, our approach
penalizes deformation, either by its Dirichlet energy or total variation.
Latter regularizer sparks the development of an alternating direction method of
multipliers on triangular meshes. Therein, a conjugate-gradients solver enables
us to bypass formation of the Gaussian normal equations appearing in the course
of the overall optimization. We combine all of the aforementioned ideas in a
versatile geometric variation-regularized Levenberg-Marquardt-type method
applicable to a variety of shape functionals, depending on intrinsic properties
of the surface such as normal field and curvature as well as its embedding into
space. Promising experimental results are reported
Shape Calculus for Shape Energies in Image Processing
Many image processing problems are naturally expressed as energy minimization
or shape optimization problems, in which the free variable is a shape, such as
a curve in 2d or a surface in 3d. Examples are image segmentation, multiview
stereo reconstruction, geometric interpolation from data point clouds. To
obtain the solution of such a problem, one usually resorts to an iterative
approach, a gradient descent algorithm, which updates a candidate shape
gradually deforming it into the optimal shape. Computing the gradient descent
updates requires the knowledge of the first variation of the shape energy, or
rather the first shape derivative. In addition to the first shape derivative,
one can also utilize the second shape derivative and develop a Newton-type
method with faster convergence. Unfortunately, the knowledge of shape
derivatives for shape energies in image processing is patchy. The second shape
derivatives are known for only two of the energies in the image processing
literature and many results for the first shape derivative are limiting, in the
sense that they are either for curves on planes, or developed for a specific
representation of the shape or for a very specific functional form in the shape
energy. In this work, these limitations are overcome and the first and second
shape derivatives are computed for large classes of shape energies that are
representative of the energies found in image processing. Many of the formulas
we obtain are new and some generalize previous existing results. These results
are valid for general surfaces in any number of dimensions. This work is
intended to serve as a cookbook for researchers who deal with shape energies
for various applications in image processing and need to develop algorithms to
compute the shapes minimizing these energies
Piecewise rigid curve deformation via a Finsler steepest descent
This paper introduces a novel steepest descent flow in Banach spaces. This
extends previous works on generalized gradient descent, notably the work of
Charpiat et al., to the setting of Finsler metrics. Such a generalized gradient
allows one to take into account a prior on deformations (e.g., piecewise rigid)
in order to favor some specific evolutions. We define a Finsler gradient
descent method to minimize a functional defined on a Banach space and we prove
a convergence theorem for such a method. In particular, we show that the use of
non-Hilbertian norms on Banach spaces is useful to study non-convex
optimization problems where the geometry of the space might play a crucial role
to avoid poor local minima. We show some applications to the curve matching
problem. In particular, we characterize piecewise rigid deformations on the
space of curves and we study several models to perform piecewise rigid
evolution of curves
The Conditional Lucas & Kanade Algorithm
The Lucas & Kanade (LK) algorithm is the method of choice for efficient dense
image and object alignment. The approach is efficient as it attempts to model
the connection between appearance and geometric displacement through a linear
relationship that assumes independence across pixel coordinates. A drawback of
the approach, however, is its generative nature. Specifically, its performance
is tightly coupled with how well the linear model can synthesize appearance
from geometric displacement, even though the alignment task itself is
associated with the inverse problem. In this paper, we present a new approach,
referred to as the Conditional LK algorithm, which: (i) directly learns linear
models that predict geometric displacement as a function of appearance, and
(ii) employs a novel strategy for ensuring that the generative pixel
independence assumption can still be taken advantage of. We demonstrate that
our approach exhibits superior performance to classical generative forms of the
LK algorithm. Furthermore, we demonstrate its comparable performance to
state-of-the-art methods such as the Supervised Descent Method with
substantially less training examples, as well as the unique ability to "swap"
geometric warp functions without having to retrain from scratch. Finally, from
a theoretical perspective, our approach hints at possible redundancies that
exist in current state-of-the-art methods for alignment that could be leveraged
in vision systems of the future.Comment: 17 pages, 11 figure
CNN-based Real-time Dense Face Reconstruction with Inverse-rendered Photo-realistic Face Images
With the powerfulness of convolution neural networks (CNN), CNN based face
reconstruction has recently shown promising performance in reconstructing
detailed face shape from 2D face images. The success of CNN-based methods
relies on a large number of labeled data. The state-of-the-art synthesizes such
data using a coarse morphable face model, which however has difficulty to
generate detailed photo-realistic images of faces (with wrinkles). This paper
presents a novel face data generation method. Specifically, we render a large
number of photo-realistic face images with different attributes based on
inverse rendering. Furthermore, we construct a fine-detailed face image dataset
by transferring different scales of details from one image to another. We also
construct a large number of video-type adjacent frame pairs by simulating the
distribution of real video data. With these nicely constructed datasets, we
propose a coarse-to-fine learning framework consisting of three convolutional
networks. The networks are trained for real-time detailed 3D face
reconstruction from monocular video as well as from a single image. Extensive
experimental results demonstrate that our framework can produce high-quality
reconstruction but with much less computation time compared to the
state-of-the-art. Moreover, our method is robust to pose, expression and
lighting due to the diversity of data.Comment: Accepted by IEEE Transactions on Pattern Analysis and Machine
Intelligence, 201
Joint Image Reconstruction and Segmentation Using the Potts Model
We propose a new algorithmic approach to the non-smooth and non-convex Potts
problem (also called piecewise-constant Mumford-Shah problem) for inverse
imaging problems. We derive a suitable splitting into specific subproblems that
can all be solved efficiently. Our method does not require a priori knowledge
on the gray levels nor on the number of segments of the reconstruction.
Further, it avoids anisotropic artifacts such as geometric staircasing. We
demonstrate the suitability of our method for joint image reconstruction and
segmentation. We focus on Radon data, where we in particular consider limited
data situations. For instance, our method is able to recover all segments of
the Shepp-Logan phantom from angular views only. We illustrate the
practical applicability on a real PET dataset. As further applications, we
consider spherical Radon data as well as blurred data
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
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