Derivation and Investigation of Affine Invariants for Image Processing Based on Wigner Distributions Open Access
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It is often of interest in computer vision to extract features from images that capture certain image information and are unchanged when the images are seen at different viewpoints. These features can be used in many computer vision applications such as object recognition and image retrieval. Affine Moment Invariants (AMI) are a specific type of features, and are defined as functions of the moments of images in the literature. AMI capture the shape information of objects in images and are unchanged when the images are seen at different affine transformations.In this dissertation a method is proposed to extract certain features of images that not only capture the shape but also texture information of objects in images and are unchanged under affine transformations. These features are called the Affine Wigner Moment Invariants (AWMI), defined as functions of the moments of the Wigner distributions of images. And they could be considered as a generalization of AMI from capturing only the shape into capturing both the shape and texture information.Specific contributions of this dissertation consist of three parts. The first part is a method generalizing the method of deriving AMI to deriving AWMI from the so-called algebraic invariants. The second part is a method to find the appropriate algebraic invariants for determining AWMI. The third part shows how to calculate AWMI from real world images, and reports two experiments. These experiments show that the AWMI are indeed affine invariant and better extract texture than AMI, and also show how AWMI can be used in image retrieval.