Foundations of semi-differential invariants

Moons, Theo; Pauwels, Eric J.; Gool, Luc J. Van; Oosterlinck, André

doi:10.1007/bf01421487

Cited by 75 publications

(52 citation statements)

References 16 publications

(16 reference statements)

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“…The moment invariants are obtained by Lie group methods (for details on Lie methods in computer vision we refer to [24,39]). Following the Lie group approach, invariants are found as solutions of systems of partial differential equations.…”

Section: Classification Of the Generalized Color Moment Invariantsmentioning

confidence: 99%

Moment invariants for recognition under changing viewpoint and illumination

Mindru

Tuytelaars

Gool

et al. 2004

Computer Vision and Image Understanding

209

115

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Generalised color moments combine shape and color information and put them on an equal footing. Rational expressions of such moments can be designed, that are invariant under both geometric deformations and photometric changes. These generalised color moment invariants are effective features for recognition under changing viewpoint and illumination. The paper gives a systematic overview of such moment invariants for several combinations of deformations and photometric changes. Their validity and potential is corroborated through a series of experiments. Both the cases of indoor and outdoor images are considered, as illumination changes tend to differ between these circumstances. Although the generalised color moment invariants are extracted from planar surface patches, it is argued that invariant neighbourhoods offer a concept through which they can also be used to deal with 3D objects and scenes.

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Section: Classification Of the Generalized Color Moment Invariantsmentioning

confidence: 99%

Moment invariants for recognition under changing viewpoint and illumination

Mindru

Tuytelaars

Gool

et al. 2004

Computer Vision and Image Understanding

209

115

View full text Add to dashboard Cite

show abstract

“…The extrema in this 3-D representation will then constitute our desired result of a set of interest points and their scales. Our procedure to construct a relative differential invariant is similar to that of [15], although that work focused on semi-differential invariants. We will denote the image f (x) by a 3-tuple of functions as…”

Section: Constructing Relative Invariantsmentioning

confidence: 99%

Extracting Scale and Illuminant Invariant Regions through Color

Unnikrishnan

Hebert

2006

Procedings of the British Machine Vision Conference 2006

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Despite the fact that color is a powerful cue in object recognition, the extraction of scale-invariant interest regions from color images frequently begins with a conversion of the image to grayscale. The isolation of interest points is then completely determined by luminance, and the use of color is deferred to the stage of descriptor formation. This seemingly innocuous conversion to grayscale is known to suppress saliency and can lead to representative regions being undetected by procedures based only on luminance. Furthermore, grayscaled images of the same scene under even slightly different illuminants can appear sufficiently different as to affect the repeatability of detections across images. We propose a method that combines information from the color channels to drive the detection of scale-invariant keypoints. By factoring out the local effect of the illuminant using an expressive linear model, we demonstrate robustness to a change in the illuminant without having to estimate its properties from the image. Results are shown on challenging images from two commonly used color constancy datasets.

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“…Furthermore, the restriction of a multi-invariant to an intermediate multi-jet subspace, as in (2.1), will define a joint differential invariant, [27] -also known as a semi-differential invariant in the computer vision literature, [9,24]. The approximation of differential invariants by joint differential invariants is, therefore, based on the extension of the differential invariant from the jet space to a suitable multi-jet subspace (2.1).…”

Section: Multi-invariantsmentioning

confidence: 99%

Geometric Foundations of Numerical Algorithms and Symmetry

Olver

2001

Applicable Algebra in Engineering, Communication and Computing

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Abstract. This paper outlines a new general construction, named "multi-space", that forms the proper geometrical foundation for the numerical analysis of differential equations -in direct analogy with the role played by jet space as the basic object underlying the geometry of differential equations. Application of the theory of moving frames leads to a general framework for constructing symmetry-preserving numerical approximations to differential invariants and invariant differential equations. †

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Foundations of semi-differential invariants

Cited by 75 publications

References 16 publications

Moment invariants for recognition under changing viewpoint and illumination

Moment invariants for recognition under changing viewpoint and illumination

Extracting Scale and Illuminant Invariant Regions through Color

Geometric Foundations of Numerical Algorithms and Symmetry

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