3,082 research outputs found
Introduction to the Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis
©1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.1998.66117
A Variational Stereo Method for the Three-Dimensional Reconstruction of Ocean Waves
We develop a novel remote sensing technique for the observation of waves on the ocean surface. Our method infers the 3-D waveform and radiance of oceanic sea states via a variational stereo imagery formulation. In this setting, the shape and radiance of the wave surface are given by minimizers of a composite energy functional that combines a photometric matching term along with regularization terms involving the smoothness of the unknowns. The desired ocean surface shape and radiance are the solution of a system of coupled partial differential equations derived from the optimality conditions of the energy functional. The proposed method is naturally extended to study the spatiotemporal dynamics of ocean waves and applied to three sets of stereo video data. Statistical and spectral analysis are carried out. Our results provide evidence that the observed omnidirectional wavenumber spectrum S(k) decays as k-2.5 is in agreement with Zakharov's theory (1999). Furthermore, the 3-D spectrum of the reconstructed wave surface is exploited to estimate wave dispersion and currents
Active Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models
Segmentation is a fundamental task for extracting semantically meaningful
regions from an image. The goal of segmentation algorithms is to accurately
assign object labels to each image location. However, image-noise, shortcomings
of algorithms, and image ambiguities cause uncertainty in label assignment.
Estimating the uncertainty in label assignment is important in multiple
application domains, such as segmenting tumors from medical images for
radiation treatment planning. One way to estimate these uncertainties is
through the computation of posteriors of Bayesian models, which is
computationally prohibitive for many practical applications. On the other hand,
most computationally efficient methods fail to estimate label uncertainty. We
therefore propose in this paper the Active Mean Fields (AMF) approach, a
technique based on Bayesian modeling that uses a mean-field approximation to
efficiently compute a segmentation and its corresponding uncertainty. Based on
a variational formulation, the resulting convex model combines any
label-likelihood measure with a prior on the length of the segmentation
boundary. A specific implementation of that model is the Chan-Vese segmentation
model (CV), in which the binary segmentation task is defined by a Gaussian
likelihood and a prior regularizing the length of the segmentation boundary.
Furthermore, the Euler-Lagrange equations derived from the AMF model are
equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image
denoising. Solutions to the AMF model can thus be implemented by directly
utilizing highly-efficient ROF solvers on log-likelihood ratio fields. We
qualitatively assess the approach on synthetic data as well as on real natural
and medical images. For a quantitative evaluation, we apply our approach to the
icgbench dataset
Photometric Depth Super-Resolution
This study explores the use of photometric techniques (shape-from-shading and
uncalibrated photometric stereo) for upsampling the low-resolution depth map
from an RGB-D sensor to the higher resolution of the companion RGB image. A
single-shot variational approach is first put forward, which is effective as
long as the target's reflectance is piecewise-constant. It is then shown that
this dependency upon a specific reflectance model can be relaxed by focusing on
a specific class of objects (e.g., faces), and delegate reflectance estimation
to a deep neural network. A multi-shot strategy based on randomly varying
lighting conditions is eventually discussed. It requires no training or prior
on the reflectance, yet this comes at the price of a dedicated acquisition
setup. Both quantitative and qualitative evaluations illustrate the
effectiveness of the proposed methods on synthetic and real-world scenarios.Comment: IEEE Transactions on Pattern Analysis and Machine Intelligence
(T-PAMI), 2019. First three authors contribute equall
Combining Contrast Invariant L1 Data Fidelities with Nonlinear Spectral Image Decomposition
This paper focuses on multi-scale approaches for variational methods and
corresponding gradient flows. Recently, for convex regularization functionals
such as total variation, new theory and algorithms for nonlinear eigenvalue
problems via nonlinear spectral decompositions have been developed. Those
methods open new directions for advanced image filtering. However, for an
effective use in image segmentation and shape decomposition, a clear
interpretation of the spectral response regarding size and intensity scales is
needed but lacking in current approaches. In this context, data
fidelities are particularly helpful due to their interesting multi-scale
properties such as contrast invariance. Hence, the novelty of this work is the
combination of -based multi-scale methods with nonlinear spectral
decompositions. We compare with scale-space methods in view of
spectral image representation and decomposition. We show that the contrast
invariant multi-scale behavior of promotes sparsity in the spectral
response providing more informative decompositions. We provide a numerical
method and analyze synthetic and biomedical images at which decomposition leads
to improved segmentation.Comment: 13 pages, 7 figures, conference SSVM 201
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