Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Electronics and Communication Sciences Unit (ECSU-Kolkata)


Majumdar, Dwijesh Dutta (ECSU-Kolkata; ISI)

Abstract (Summary of the Work)

The problems of detection and use of reflectional symmetry in the images of planar shape contours are studied. Symmetry, in general, provides important shape representation cues, some of which we utilise here, to acquire viewpoint information and, towards model based shape matching. We concentrate on local reflectional symmetries of emoothly curved planar objecta, though the methoda are equally applicable to polygonal objects; even this could be extended to certain three-dimensional shapes and for other object relations such as rotational symmetry.Under the affine or perspective approximation to image projection, properties of geometrie invariance are used to find (reflectional) symmetric contour pairs. Local symmetry line in detected from the transformation matrix (responsible for inter-symmetric-curve reflection) of symmetric contour pair. The key result we establiah here, is that due to bilateral symmetry constraint, the image tranaformation between the symmetric contour pair is a subact of affine or projective transformation, s the case of image projection may be. The goal of the analysis, at this stage, is to remore the imaged distortion (perspective fanning and Bfine skewing) due to the affine or perspective approximation to image projection. This is to recover the shape of the object up to similarity transform (rotation, translation and isotropic scaling) ambiguity, Symmetry constraint is utilised to ind the back-projection matrix responsible for image distortion. This image-to-object transformation (up to similarity ambiguity) in used to determine the object plane orientations relative to the camera and, to test for non-co-planarity among at a collection of objects.As we establish algorithma for obtaining back-projected images from the skewed scene, we concentrate on the wave diffusion algorithm which gives almost all the perceptually relevant symmetry set for planar abapen up to similarity transform. We study thin symmetry generation process and present the parallel implementation of this methodology on a transputer network. Thin is to overcome the basic drawback of wave diffusion process, vix. the high processing time. An attractive alternative, almost instantaneous, for symmetry set generation, we call normal tranaform, similar to the wave propagation mechanism in introduced.Symmetry set of a planar shape, generated uning wave diffusion procem, is used for model based symmetry set matching. Symmetry seta of tbe image and the models are transformed to a representative frame to take care of images of objecta up to similarity tranaform. The structural and relational matching constraints between the symmetry set of an image and the symmetry neta of models, combined together, are incorporated in an energy function.Simulated annealing technique is used to minimize this energy function to ind the beat match.The thesis in concluded by a summary indicating the future ncope of research.


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Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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