Object-Image Metrics for Generalized Weak Perspective Projection

Arnold, Gregory; Stiller, Peter F.; Sturtz, Kirk

doi:10.1007/0-8176-4481-4_10

Cited by 12 publications

(17 citation statements)

References 18 publications

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“…As far as affine shape is concerned, we examined the shape spaces for that larger groups of transformations in previous work (see Stiller [6]) and explored the relationship between the shape of a configuration of points in three dimensions and the shapes of all the images of that configuration in two dimensions under all possible generalized weak perspective projections. This led to the notion of the object/image equations which quantify the relationship between 3D object features (points) and 2D image features.…”

Section: Shape Spaces and Object/image Relationsmentioning

confidence: 99%

Statistical shape analysis for image understanding and object recognition

Stiller

2014

Image Processing: Algorithms and Systems XII

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In order to analyze the effects of noise on certain recognition and reconstruction algorithms, including the sensitivity of the so-called object/image equations and object/image metrics, one needs to study probability and statistics on shape spaces. Work along these lines was pioneered by Kendall and has been the subject of many papers over the last twenty years. In this paper we extend some of those results to affine shape spaces and then use them to relate distributions on object shapes to corresponding distributions on image shapes.

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Section: Shape Spaces and Object/image Relationsmentioning

confidence: 99%

Statistical shape analysis for image understanding and object recognition

Stiller

2014

Image Processing: Algorithms and Systems XII

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“…For example, if our feature set is an r-tuple of points we will have R 3r or P 3 R × ... × P 3 R (an r-fold product of projective spaces) as our parameter space for possible arrangements of features. Lines in space can be parameterized by an open subset of the four dimensional Grassmann manifold Gr (2,4). We will denote by X and Y the object and image feature spaces respectively.…”

Section: Basic Theorymentioning

confidence: 99%

Invariant methods for real-time object recognition and image understanding

Stiller

2012

SPIE Proceedings

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In this paper we discuss certain recently developed invariant geometric techniques that can be used for fast object recognition or fast image understanding. The results make use of techniques from algebraic geometry that allow one to relate the geometric invariants of a feature set in 3D to similar invariants in 2D or 1D. The methods apply equally well to optical images or radar images. In addition to the "object/image" equations relating these invariants, we also discuss certain invariant metrics and show why they provide a more natural and robust test for matching object features to image features. Additional aspects of the work as it applies to shape reconstruction and shape statistics will also be explored.

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“…Such a measure (or metric) is described in. 9 It was developed earlier using techniques in shape theory. The essential question then becomes: how far apart are two object shapes or two image shapes?…”

Section: An Example Of An Object-image Metricmentioning

confidence: 99%

Further exploration of the object-image metric with image registration in mind

2008

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An object-image metric is an extension of standard metrics in that it is constructed for matching and comparing configurations of object features to configurations of image features. For the generalized weak perspective camera, it is invariant to any affine transformation of the object or the image. Recent research in the exploitation of the object-image metric suggests new approaches to Automatic Target Recognition (ATR). This paper explores the object-image metric and its limitations. Through a series of experiments, we specifically seek to understand how the object-image metric could be applied to the image registration problem-an enabling technology for ATR.

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Object-Image Metrics for Generalized Weak Perspective Projection

Cited by 12 publications

References 18 publications

Statistical shape analysis for image understanding and object recognition

Statistical shape analysis for image understanding and object recognition

Invariant methods for real-time object recognition and image understanding

Further exploration of the object-image metric with image registration in mind

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