Projective and illumination invariant representation of disjoint shapes

Abstract

We describe a new projectively invariant representation of disjoint contour groups which is suitable for shape-based retrieval from an image database. It consists of simultaneous polar reparametrization of multiple curves where an invariant point is used as the origin. For each ray orientation, a cross-ratio of its intersections with other curves is taken as a value associated to the radius. With respect to other methods this representation is less reliant on single curve properties, both for the construction of the projective basis and for calculating the signature. It is therefore more robust to contour gaps and image noise and is better suited to describing complex planar shapes defined by multiple disjoint curves. The proposed representation has been originally developed for planar shapes, but an extension is proposed and validated for 3D faceted objects. Moreover, we show that illumination invariance fits well within the proposed framework and can easily be introduced in the representation in order to make it more appropriate for shape-based retrieval. Experiments are reported on a database of real trademarks

A Rotation, Translation, and Scale-Invariant Approach to Content-Based Image Retrieval

“…Indeed, the shots from which all query images were selected present complex tracking and dollying motion (in addition to pan/tilt/zoom, producing RTS transformations) that would in principle require more complex and computationally time-consuming geometric models for signature extraction (cf. [14]). Furthermore, subject motion causes objects to enter and leave the camera field of view, thereby altering the image content.…”

“…In general, the changes induced by object and camera motion are not restricted to this type of transformation (cf. [14] for an alternative representation that is invariant to affine and projective transformations). However, experimental results from a large database of heterogeneous videos show that it provides a good approximation to invariance under more general, nonrigid transformations.…”

Invariant Content-Based Image Retrieval Using the Fourier-Mellin Transform

“…In general, the changes induced by object and camera motion are not restricted to this type of transformation (cf. [3] for an alternative representation that is invariant to ane and projective transformations). However, experimental results from a large database of heterogeneous videos show that it provides a good approximation to invariance under more general, non-rigid transformations.…”

“…Indeed, the shots from which all query images where selected present complex tracking and dollying motion (in addition to pan/tilt/zoom producing RTS transformations) that would in principle require more complex and computationally time-consuming geometric models for signature extraction (cf. [3]). Furthermore, subject motion causes objects to enter and leave the camera eld of view, thereby altering the image content.…”

Robust Homography Estimation from Planar Contours Based on Convexity

“…Most of the proposed solutions for curve matching are based on differential properties [5,6,7,8,9] or in specific contour models [10,11], which cannot be directly used over low quality images The projective geometry of multiple views of curves has been studied in [12]. Invariant signatures based on rays have been proposed in [13] to retrieve shapes in a database of trademarks. Application of contour matching to visual servoing using snakes is described in [14], where weak perspective estimates, point redistribution, and projective correction steps are iterated until convergence.…”