A Representation for Shape Based on Peaks and Ridges in the Difference of Low-Pass Transform

Crowley, James L.; Parker, Alice C.

doi:10.1109/tpami.1984.4767500

Cited by 233 publications

(105 citation statements)

References 14 publications

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“…Medical applications of the scale-space primal sketch have been developed for analyzing functional brain activation images (Lindeberg et al [117], Coulon et al [29], Rosbacke et al [136], Mangin et al [120]) and for capturing the folding patterns of the cortical surface (Cachia et al [25]). More algorithmically based work on building graphs of blob and ridge features at different scales was presented by Crowley and his co-workers [31,32] using difference of low-pass features defined from a pyramid; hence with very close similarities to differencesof-Gaussians operators and thus the Laplacian.…”

Section: Related Workmentioning

confidence: 99%

Image Matching Using Generalized Scale-Space Interest Points

Lindeberg

2013

Lecture Notes in Computer Science

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The performance of matching and object recognition methods based on interest points depends on both the properties of the underlying interest points and the choice of associated image descriptors. This paper demonstrates advantages of using generalized scale-space interest point detectors in this context for selecting a sparse set of points for computing image descriptors for image-based matching. For detecting interest points at any given scale, we make use of the Laplacian ∇ 2 norm L, the determinant of the Hessian det H norm L and four new unsigned or signed Hessian feature strength measures D 1,norm L,D 1,norm L, D 2,norm L and D 2,norm L, which are defined by generalizing the definitions of the Harris and Shi-and-Tomasi operators from the second moment matrix to the Hessian matrix. Then, feature selection over different scales is performed either by scale selection from local extrema over scale of scale-normalized derivates or by linking features over scale into feature trajectories and computing a significance measure from an integrated measure of normalized feature strength over scale. A theoretical analysis is presented of the robustness of the differential entities underlying these interest points under image deformations, in terms of invariance properties under affine image deformations or approximations thereof. Disregarding the effect of the rotationally symmetric scale-space smoothing operation, the determinant of the Hessian det H norm L is a truly affine covariant differential entity and the Hessian feature strength measures D 1,norm L andD 1,norm L have a major contribution from the affine covariant determinant of the Hessian, implying that local extrema of these differen- It is shown how these generalized scale-space interest points allow for a higher ratio of correct matches and a lower ratio of false matches compared to previously known interest point detectors within the same class. The best results are obtained using interest points computed with scale linking and with the new Hessian feature strength measures D 1,norm L,D 1,norm L and the determinant of the Hessian det H norm L being the differential entities that lead to the best matching performance under perspective image transformations with significant foreshortening, and better than the more commonly used Laplacian operator, its difference-of-Gaussians approximation or the Harris-Laplace operator. We propose that these generalized scale-space interest points, when accompanied by associated local scale-invariant image descriptors, should allow for better performance of interest point based methods for image-based matching, object recognition and related visual tasks.

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Section: Related Workmentioning

confidence: 99%

Image Matching Using Generalized Scale-Space Interest Points

Lindeberg

2013

Lecture Notes in Computer Science

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“…The algorithm begins by forming a n 1 × n 2 2 , assuming that u and v are compatible in terms of their shock order, and has the value ∞ otherwise. 6 Next, we form a bipartite edge weighted graph G (V 1 , V 2 , E G ) with edge weights from the matrix Π (G, H).…”

Section: Algorithm For Matching Two Shock Treesmentioning

confidence: 99%

“…Another related approach is due to Crowley et al [3,2,4]. From a Laplacian pyramid computed on an image, peaks and ridges at each scale are detected as local maxima.…”

Section: Selected Related Workmentioning

confidence: 99%

Graph-Theoretical Methods in Computer Vision

Shokoufandeh

Dickinson

2002

Theoretical Aspects of Computer Science

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Abstract. The management of large databases of hierarchical (e.g., multi-scale or multilevel) image features is a common problem in object recognition. Such structures are often represented as trees or directed acyclic graphs (DAGs), where nodes represent image feature abstractions and arcs represent spatial relations, mappings across resolution levels, component parts, etc. Object recognition consists of two processes: indexing and verification. In the indexing process, a collection of one or more extracted image features belonging to an object is used to select, from a large database of object models, a small set of candidates likely to contain the object. Given this relatively small set of candidates, a verification, or matching procedure is used to select the most promising candidate. Such matching problems can be formulated as largest isomorphic subgraph or largest isomorphic subtree problems, for which a wealth of literature exists in the graph algorithms community. However, the nature of the vision instantiation of this problem often precludes the direct application of these methods. Due to occlusion and noise, no significant isomorphisms may exists between two graphs or trees. In this paper, we review our application of spectral encoding of a graph for indexing to large database of image features represented as DAGs. We will also review a more general class of matching methods, called bipartite matching, to two problems in object recognition.

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“…(Crowley & Parker 1984, Crowley & Sanderson 1987) detected peaks and ridges in a pyramid representation. In retrospect, a main reason why stability problems were encountered is that the pyramids involved a rather coarse sampling in the scale direction.…”

Section: Choice Of Image Representation For Feature Trackingmentioning

confidence: 99%

Qualitative Multi-scale Feature Hierarchies for Object Tracking

Bretzner¹,

Lindeberg²

1999

Scale-Space Theories in Computer Vision

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This paper shows how the performance of feature trackers can be improved by building a hierarchical view-based object representation consisting of qualitative relations between image structures at different scales. The idea is to track all image features individually, and to use the qualitative feature relations for avoiding mismatches, resolving ambiguous matches and for introducing feature hypotheses whenever image features are lost. Compared to more traditional work on view-based object tracking, this methodology has the ability to handle semi-rigid objects and partial occlusions. Compared to trackers based on threedimensional object models, this approach is much simpler and of a more generic nature. A hands-on example is presented showing how an integrated application system can be constructed from conceptually very simple operations.

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A Representation for Shape Based on Peaks and Ridges in the Difference of Low-Pass Transform

Cited by 233 publications

References 14 publications

Image Matching Using Generalized Scale-Space Interest Points

Image Matching Using Generalized Scale-Space Interest Points

Graph-Theoretical Methods in Computer Vision

Qualitative Multi-scale Feature Hierarchies for Object Tracking

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