Planar object recognition under geometric transformations using wavelet transform

This thesis provides recognition systems to identify planar objects under different geometric transformations using the wavelet transform. The geometric transformations such as similarity, affine and perspective transformations are considered. Both continuous and dyadic wavelet transforms are used for the developed algorithms.; To recognize 2D objects, which are subjected to orientation, location, and size transformations, two schemes are presented. The first scheme uses the zero crossing of the dyadic wavelet transform to characterize the boundary Θ - S diagram. The wrap around error in the Θ - S diagram is eliminated before applying the wavelet transform. A “Structured Neural Network” is used for the classification process. The second scheme uses the modulus maxima of continuous wavelet transform. An algorithm is proposed to extract a feature vector for the singularities in the Θ - S diagram. The feature vector characterizes the singularities in the object boundary. The feature vector is composed of the Lipschitz exponent of each singularity and the distances between these singularities. In order to evaluate the performance of the recognition systems, real object-sets are used. The effectiveness of the recognition systems is tested by adding random Gaussian noise to the shape boundary points.; Affine invariant functions are derived using the dyadic wavelet transform to recognize objects under affine transformation. An affine invariant function is derived using two dyadic levels. This invariant function is used to derive another invariant function that uses four dyadic levels. A wavelet-based conic equation is introduced. This equation is used to derive two relative affine invariant functions. The first of these functions uses three dyadic levels and the other one uses six dyadic levels. Experiments are carried out to test the invariant functions. These experiments are designed to test (i) the discrimination power of the proposed invariant functions, (ii) the behavior of the invariant functions under large perspective transformation, (iii) the stability of the invariant functions, and (iv) the performance of the invariant functions as compared to some traditional methods on synthetic data.; Finally, a perspective invariant scheme is given to recognize objects under a perspective transformation. Experiments are carried out to discuss the dyadic scales used in the proposed invariant function. These are then used to test the discrimination power of the proposed invariant function, and to investigate the stability of the invariant function.