On the Foundations of Relaxation Labeling Processes

Hummel, Robert A.; Zucker, Steven W.

doi:10.1109/tpami.1983.4767390

Cited by 773 publications

(156 citation statements)

References 10 publications

Supporting

Mentioning

155

Contrasting

Unclassified

Order By: Relevance

“…, h n }. We use relaxation labeling [8] to determine which of the possible flows h i offers the best local fit to the fold lines of the cortical surface. Relaxation labeling is a framework to find the statistical mode of a distribution given general constraints to be satisfied.…”

Section: Relaxation Labeling Of Tangential and Normal Curvaturementioning

confidence: 99%

See 1 more Smart Citation

A Texture Manifold for Curve-Based Morphometry of the Cerebral Cortex

Boucher

Evans

Siddiqi

2011

Medical Computer Vision. Recognition Techniques and Applications in Medical Imaging

View full text Add to dashboard Cite

Abstract. The cortical surface of the human brain is composed of folds that are juxtaposed alongside one another. Several methods have been proposed to study the shape of these folds, e.g., by first segmenting them on the cortical surface or by analysis via a continuous deformation of a common template. A major disadvantage of these methods is that, while they can localize shape differences, they cannot easily identify the directions in which they occur. The type of deformation that causes a fold to change in length is quite different from that which causes it to change in width. Furthermore, these two deformations may have a completely different biological interpretation. In this article we propose a method to analyze such deformations using directional filters locally adapted to the geometry of the folding pattern. Motivated by the texture flow literature in computer vision we recover flow fields that maintain a fixed angle with the orientation of folds, over a significant spatial extent. We then trace the flow fields to determine which correspond to the shape changes that are the most salient. Using the OASIS database, we demonstrate that in addition to known regions of atrophy, our method can find subtle but statistically significant shape deformations.

show abstract

Section: Relaxation Labeling Of Tangential and Normal Curvaturementioning

confidence: 99%

“…where the p i 2 term is added to make the relaxation labeling scheme converge to an unambiguous labeling, i.e., p i = {0, 1}, as explained in [8].…”

Section: Figmentioning

confidence: 99%

A Texture Manifold for Curve-Based Morphometry of the Cerebral Cortex

Boucher

Evans

Siddiqi

2011

Medical Computer Vision. Recognition Techniques and Applications in Medical Imaging

View full text Add to dashboard Cite

show abstract

“…Multi-Standard Quadratic Problems arise in diverse fields of applications, like relaxation labelling processes for speech and pattern recognition, see Hummel and Zucker [7] and Pelillo [13], and machine learning (support vector machines for classification). Recently two monotonely improving interior point methods have been proposed and also a conic reformulation has been established to obtain rigid yet relatively cheap bounds via semidefinite programming, see Bomze et al [2] and Burer [4].…”

Section: Multi-standard Quadratic Problemsmentioning

confidence: 99%

A Conic Duality Frank–Wolfe-Type Theorem via Exact Penalization in Quadratic Optimization

Schachinger

Bomze

2009

Mathematics of OR

View full text Add to dashboard Cite

Abstract. The famous Frank-Wolfe theorem ensures attainability of the optimal value for quadratic objective functions over a (possibly unbounded) polyhedron if the feasible values are bounded. This theorem does not hold in general for conic programs where linear constraints are replaced by more general convex constraints like positive-semidefiniteness or copositivity conditions, despite the fact that the objective can be even linear. This paper studies exact penalizations of (classical) quadratic programs, i.e. optimization of quadratic functions over a polyhedron, and applies the results to establish a Frank-Wolfe type theorem for the primal-dual pair of a class of conic programs which frequently arises in applications. One result is that uniqueness of the solution of the primal ensures dual attainability, i.e., existence of the solution of the dual.

show abstract

“…Such relaxation techniques have wide use in computer vision and are based upon an iterative scheme that enhances edge responses if neighborhood responses are strong and that inhibits the response if neighborhood outputs are weak (see Hummel & Zucker, 1983).…”

Section: Image-feature Extractionmentioning

confidence: 99%