31,675 research outputs found
Estimation of vector fields in unconstrained and inequality constrained variational problems for segmentation and registration
Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between
objects, and the contour or surface that defines the segmentation of the objects as well.We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector
field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and
segmentation. We present both the theory and results that demonstrate our approach
Image Segmentation Using Weak Shape Priors
The problem of image segmentation is known to become particularly challenging
in the case of partial occlusion of the object(s) of interest, background
clutter, and the presence of strong noise. To overcome this problem, the
present paper introduces a novel approach segmentation through the use of
"weak" shape priors. Specifically, in the proposed method, an segmenting active
contour is constrained to converge to a configuration at which its geometric
parameters attain their empirical probability densities closely matching the
corresponding model densities that are learned based on training samples. It is
shown through numerical experiments that the proposed shape modeling can be
regarded as "weak" in the sense that it minimally influences the segmentation,
which is allowed to be dominated by data-related forces. On the other hand, the
priors provide sufficient constraints to regularize the convergence of
segmentation, while requiring substantially smaller training sets to yield less
biased results as compared to the case of PCA-based regularization methods. The
main advantages of the proposed technique over some existing alternatives is
demonstrated in a series of experiments.Comment: 27 pages, 8 figure
Combinatorial Continuous Maximal Flows
Maximum flow (and minimum cut) algorithms have had a strong impact on
computer vision. In particular, graph cuts algorithms provide a mechanism for
the discrete optimization of an energy functional which has been used in a
variety of applications such as image segmentation, stereo, image stitching and
texture synthesis. Algorithms based on the classical formulation of max-flow
defined on a graph are known to exhibit metrication artefacts in the solution.
Therefore, a recent trend has been to instead employ a spatially continuous
maximum flow (or the dual min-cut problem) in these same applications to
produce solutions with no metrication errors. However, known fast continuous
max-flow algorithms have no stopping criteria or have not been proved to
converge. In this work, we revisit the continuous max-flow problem and show
that the analogous discrete formulation is different from the classical
max-flow problem. We then apply an appropriate combinatorial optimization
technique to this combinatorial continuous max-flow CCMF problem to find a
null-divergence solution that exhibits no metrication artefacts and may be
solved exactly by a fast, efficient algorithm with provable convergence.
Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the
fact, already proved by Nozawa in the continuous setting, that the max-flow and
the total variation problems are not always equivalent.Comment: 26 page
A higher-order active contour model of a `gas of circles' and its application to tree crown extraction
Many image processing problems involve identifying the region in the image
domain occupied by a given entity in the scene. Automatic solution of these
problems requires models that incorporate significant prior knowledge about the
shape of the region. Many methods for including such knowledge run into
difficulties when the topology of the region is unknown a priori, for example
when the entity is composed of an unknown number of similar objects.
Higher-order active contours (HOACs) represent one method for the modelling of
non-trivial prior knowledge about shape without necessarily constraining region
topology, via the inclusion of non-local interactions between region boundary
points in the energy defining the model. The case of an unknown number of
circular objects arises in a number of domains, e.g. medical, biological,
nanotechnological, and remote sensing imagery. Regions composed of an a priori
unknown number of circles may be referred to as a `gas of circles'. In this
report, we present a HOAC model of a `gas of circles'. In order to guarantee
stable circles, we conduct a stability analysis via a functional Taylor
expansion of the HOAC energy around a circular shape. This analysis fixes one
of the model parameters in terms of the others and constrains the rest. In
conjunction with a suitable likelihood energy, we apply the model to the
extraction of tree crowns from aerial imagery, and show that the new model
outperforms other techniques
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
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