Results 1  10
of
298
ApertureAngle and HausdorffApproximation of Convex Figures ∗
"... The aperture angle α(x, Q) of a point x ̸ ∈ Q in the plane with respect to a convex polygon Q is the angle of the smallest cone with apex x that contains Q. The aperture angle approximation error of a compact convex set C in the plane with respect to an inscribed convex polygon Q ⊂ C is the minimum ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The aperture angle α(x, Q) of a point x ̸ ∈ Q in the plane with respect to a convex polygon Q is the angle of the smallest cone with apex x that contains Q. The aperture angle approximation error of a compact convex set C in the plane with respect to an inscribed convex polygon Q ⊂ C is the minimum
Convex Optimization for Image Segmentation
"... Segmentation is one of the fundamental low level problems in computer vision. Extracting objects from an image gives rise to further high level processing as well as image composing. A segment not always has to correspond to a real world object, but can fulfill any coherency criterion (e.g. similar ..."
Abstract
 Add to MetaCart
of these problems. Continuous energy minimization provides an elegant way to model a problem like image segmentation. If the problem is convex, there are powerful optimization algorithms available. Additionally, we are guaranteed to find the globally optimal solution. We give an extensive introduction to convex
4D deformable models with temporal constraints: application to 4D cardiac image segmentation
, 2005
"... ..."
Manifold reconstruction in arbitrary dimensions using witness complexes
 In Proc. 23rd ACM Sympos. on Comput. Geom
, 2007
"... It is a wellestablished fact that the witness complex is closely related to the restricted Delaunay triangulation in low dimensions. Specifically, it has been proved that the witness complex coincides with the restricted Delaunay triangulation on curves, and is still a subset of it on surfaces, und ..."
Abstract

Cited by 39 (11 self)
 Add to MetaCart
It is a wellestablished fact that the witness complex is closely related to the restricted Delaunay triangulation in low dimensions. Specifically, it has been proved that the witness complex coincides with the restricted Delaunay triangulation on curves, and is still a subset of it on surfaces, under mild sampling assumptions. Unfortunately, these results do not extend to higherdimensional manifolds, even under stronger sampling conditions. In this paper, we show how the sets of witnesses and landmarks can be enriched, so that the nice relations that exist between both complexes still hold on higherdimensional manifolds. We also use our structural results to devise an algorithm that reconstructs manifolds of any arbitrary dimension or codimension at different scales. The algorithm combines a farthestpoint refinement scheme with a vertex pumping strategy. It is very simple conceptually, and it does not require the input point sample W to be sparse. Its time complexity is bounded by c(d)W  2, where c(d) is a constant depending solely on the dimension d of the ambient space. 1
Depth And Motion Discontinuities
, 1999
"... Depth and motion discontinuities arise wherever a light ray incident on a camera sensor meets a discrete change in the depth or motion of the surfaces in the world. Because these discontinuities tend to coincide with occlusions and with the boundaries of objects, they provide useful information for ..."
Abstract

Cited by 25 (1 self)
 Add to MetaCart
Depth and motion discontinuities arise wherever a light ray incident on a camera sensor meets a discrete change in the depth or motion of the surfaces in the world. Because these discontinuities tend to coincide with occlusions and with the boundaries of objects, they provide useful information for a number of applications in computer vision, such as camera control, compression, and tracking. Moreover, because they have simple, precise definitions depending only upon the physics of the scene, they are unaffected by subjective considerations. The first part of this thesis presents an algorithm to detect depth discontinuities from a stereo pair of images by matching pixels in corresponding scanlines and then propagating information between those scanlines. It uses a new measure of pixel dissimilarity that is provably insensitive to image sampling. The algorithm is fast and is shown to produce good results on difficult images containing untextured, slanted surfaces. Then some work aimed a...
Optimization · Manifold valued
"... Abstract We introduce a general framework for regularization of signals with values in a cyclic structure, such as angles, phases or hue values. These include the total cyclic variation TV S 1, as well as cyclic versions of quadratic regularization, HuberTV and MumfordShah regularity. The key idea ..."
Abstract
 Add to MetaCart
Abstract We introduce a general framework for regularization of signals with values in a cyclic structure, such as angles, phases or hue values. These include the total cyclic variation TV S 1, as well as cyclic versions of quadratic regularization, HuberTV and MumfordShah regularity. The key
Learning from One Example in Machine Vision by Sharing Probability Densities
, 2002
"... Human beings exhibit rapid learning when presented with a small number of images of a new object. A person can identify an object under a wide variety of visual conditions after having seen only a single example of that object. This ability can be partly explained by the application of previously le ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
Human beings exhibit rapid learning when presented with a small number of images of a new object. A person can identify an object under a wide variety of visual conditions after having seen only a single example of that object. This ability can be partly explained by the application of previously learned statistical knowledge to a new setting. This thesis presents an approach to acquiring knowledge in one setting and using it in another. Specifically, we develop probability densities over common image changes. Given a single image of a new object and a model of change learned from a di#erent object, we form a model of the new object that can be used for synthesis, classification, and other visual tasks. We start by
Results 1  10
of
298