General intensity transformations and differential invariants

Florack, Luc; Romeny, BM Bart ter Haar; Koenderink, Jan J.; Viergever, MA Max

doi:10.1007/bf01249895

Cited by 126 publications

(75 citation statements)

References 15 publications

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“…For instance, since image intrinsic properties must be coordinate independent, a question arises about its implications for the construction of image differential invariants [13][14][15] and tensor calculus. A second question pertains to the extension of standard variational techniques for image optimization problems to the multiplicative case.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Multiplicative Calculus in Biomedical Image Analysis

2011

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We advocate the use of an alternative calculus in biomedical image analysis, known as multiplicative (a.k.a. non-Newtonian) calculus. It provides a natural framework in problems in which positive images or positive definite matrix fields and positivity preserving operators are of interest. Indeed, its merit lies in the fact that preservation of positivity under basic but important operations, such as differentiation, is manifest. In the case of positive scalar functions, or in general any set of positive definite functions with a commutative codomain, it is a convenient, albeit arguably redundant framework. However, in the increasingly important non-commutative case, such as encountered in diffusion tensor imaging and strain tensor analysis, multiplicative calculus complements standard calculus in a truly nontrivial way. The purpose of this article is to provide a condensed review of multiplicative calculus and to illustrate its potential use in biomedical image analysis.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Multiplicative Calculus in Biomedical Image Analysis

2011

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“…Gauge derivatives can be transformed back to an arbitrary Cartesian coordinate system by a gradient dependent rotation, cf. [9] for details.) The invariant w (0) is the well-known isophote curvature.…”

Section: General Grey-scale Invariantsmentioning

confidence: 99%

“…The invariants proposed by Florack et al [9] are based on the local isophote structure of an image. Isophotes are curves (in 2D) of constant grey-value u in an image, and their shape is invariant under the group of invertible intensity transformations, u → γ (u) with γ = 0.…”

Section: General Grey-scale 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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“…First, the fast-Hessian corner detector [16], which is based on integral image and approximation, is performed. The Hessian matrix is responsible for primary image rotation ( Figure 3) using principal points that are identified as being of interest.…”

Section: Significant Featuresmentioning

confidence: 99%

Automatic Registration of Airborne and Spaceborne Images by Topology Map Matching with SURF Processor Algorithm

Brook

Ben‐Dor

2011

Remote Sensing

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Abstract:Image registration is widely used in remote-sensing applications. The existing automatic image registration techniques fall into two categories: Intensity-based and feature-based; the latter (which extracts structures from both images) being more suitable for multi-sensor fusion, detection of temporal changes and image mosaicking. Conventional image registration algorithms have proven to be inaccurate, time-consuming, and unfeasible due to image complexity which makes it cumbersome or even impossible to discern the appropriate control points. In this study, we propose a novel method for automatic image registration based on topology (AIRTop) for change detection and multi-sensor (airborne and spaceborne) fusion. In this algorithm, we first apply image-processing methods (SURF-Speeded-Up Robust Features) to extract the landmark structures (roads and buildings) and convert them to a features (vector) map. The following stages are applied in GIS (Geographic Information System), where topology rules, which define the permissible spatial relationships between features, are defined. The relationships between features are established by weight-based topological map-matching algorithm (tMM). The suggested algorithm presents a robust method for image registration. The main focus in this study is on scale and image rotation, when the quality of the scanning system is constant. These seem to offer a good compromise between feature complexity and robustness to commonly occurring deformations. The skew and the anisotropic scaling are assumed to be second-order effects that are covered to some degree by the overall robustness of the sensor. OPEN ACCESSRemote Sens. 2011, 3 66 Keywords: automatic registration; multi-sensor airborne and spaceborne fusion; change detection; weight-based topological map-matching algorithm (tMM); scaling and image rotation

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General intensity transformations and differential invariants

Cited by 126 publications

References 15 publications

Multiplicative Calculus in Biomedical Image Analysis

Multiplicative Calculus in Biomedical Image Analysis

Novel Similarity Measures for Differential Invariant Descriptors for Generic Object Retrieval

Automatic Registration of Airborne and Spaceborne Images by Topology Map Matching with SURF Processor Algorithm

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