Cartesian differential invariants in scale-space

Florack, Luc; Romeny, ter Bm Bart Haar; Koenderink, Jan J.; Viergever, Max A.

doi:10.1007/bf01664793

Cited by 80 publications

(56 citation statements)

References 22 publications

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“…without violating the causality principle [136]. As such, one can apply to LOIs the whole machinery of techniques that has been developed in the context of scale-space research, such as the N-jet for local image structure description [137,70,94], the construction of invariants and (oriented) filter families [138,139,140,71], non-linear diffusion schemes [195,93], scale selection methods [160,161], etc.…”

Section: Discussionmentioning

confidence: 99%

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Computer aided diagnosis in chest radiography

Mouton¹,

Douglas

2003

Academic Radiology

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Section: Discussionmentioning

confidence: 99%

“…The use of Gaussian receptive field families allows one to directly use results of scale-space theory to construct filters which are invariant to rotations [71] and gray-level transformations [69], if desired.…”

Section: Filter Banksmentioning

confidence: 99%

Computer aided diagnosis in chest radiography

Mouton¹,

Douglas

2003

Academic Radiology

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“…One of the ways to avoid this problem is to choose one particular, geometrically meaningful coordinate system, and to compute the local jet components (which are then invariants by construction) as partial image derivatives relative this system. Blom [4] and Florack et al [8] proposed to use a gauge coordinate system as a right handed local frame, in which one axis (ordinate component: w) points in the same direction as the local image gradient, and the other axis (abscissa component: v) is tangential to the isophote. The N -jet at a given base point has a finite number of independent degrees of freedom.…”

Section: Cartesian Invariantsmentioning

confidence: 99%

Novel Similarity Measures for Differential Invariant Descriptors for Generic Object Retrieval

Balmashnova

Florack

2008

J Math Imaging Vis

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Local feature matching is an essential component of many image and object retrieval algorithms. Euclidean and Mahalanobis distances are mostly used in order to quantify the similarity of two stipulated feature vectors. The Euclidean distance is inappropriate in the typical case where the components of the feature vector are incommensurable entities, and indeed yields unsatisfactory results in practice. The Mahalanobis distance performs better, but is less generic in the sense that it requires specific training data.In this paper we consider two alternative ways to construct generic distance measures for image and object retrieval, which do not suffer from any of these shortcomings. The first approach aims at obtaining a (image independent) covariance matrix for a Mahalonobis-like distance function without explicit training, and is applicable to feature vectors consisting of partial image derivatives. In the second approach a stability based similarity measure (SBSM) is introduced for feature vectors that are composed of arbitrary algebraic combinations of image derivatives, and likewise requires no explicit training. The strength and novelty of SBSM lies in the fact that the associated covariance matrix exploits local image structure. A performance analysis shows that feature matching based on SBSM outperforms algorithms based on Euclidean and Mahalanobis distances.

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“…The complete sets proposed by Florack et al [6] are invariant to rigid transformations. By suitable scaling and normalization we obtain invariance to spatial zooming and intensity scaling as well, but the resulting system has the property that most low order invariants vanish identically at the top-points of the original (zeroth order) image, and thus do not qualify as distinctive features.…”

Section: Local Invariant Featuresmentioning

confidence: 99%

“…The choice of invariant features taken in the top-points is free. Because of their simple and mathematically nice nature we have chosen to use a complete set of differential invariants up to third order [5,6] as invariant features. A similarity measure between these invariant feature vectors based on the noise behavior of the differential invariants is proposed.…”

Section: Introductionmentioning

confidence: 99%

Using Top-Points as Interest Points for Image Matching

Platel

Balmachnova

Florack

et al. 2005

Lecture Notes in Computer Science

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Abstract. We consider the use of so-called top-points for object retrieval. These points are based on scale-space and catastrophe theory, and are invariant under gray value scaling and offset as well as scale-Euclidean transformations. The differential properties and noise characteristics of these points are mathematically well understood. It is possible to retrieve the exact location of a top-point from any coarse estimation through a closed-form vector equation which only depends on local derivatives in the estimated point. All these properties make top-points highly suitable as anchor points for invariant matching schemes. In a set of examples we show the excellent performance of top-points in an object retrieval task.

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Cartesian differential invariants in scale-space

Cited by 80 publications

References 22 publications

Computer aided diagnosis in chest radiography

Computer aided diagnosis in chest radiography

Novel Similarity Measures for Differential Invariant Descriptors for Generic Object Retrieval

Using Top-Points as Interest Points for Image Matching

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