Introduction

The interest in automatic analysis of images based upon their content has increased with recent developments in the World Wide Web (WWW), digital image collections, networking and multimedia. Active research in content-based image retrieval (CBIR) is geared towards the development of methodologies for analyzing, interpreting, cataloging and indexing image databases. In image analysis, the input and output are functions of $\Re^2$, and an appropriate notion of isotropy of computations is the Euclidean invariance: any rotation, translation or reflection of the input should produce an identical result under these transformations, thus achieving orientation and position invariance. These image transformations are generated by the action of the planar Euclidean group (the semi-direct product of the orthogonal group and the translation group). Using this notion of isotropy, we present an approach for content-based image retrieval via isotropic and anisotropic mappings.

We define an isotropic mapping as a mapping that is invariant to the action of the Euclidean group - invariant to translation, rotation, and reflection of image data. Similarly, we define an anisotropic mapping as a mapping that is variant to the action of the Euclidean group. The Euclidean group is the group of isometries of $\Re^2$ - mappings that preserve distances - and its action on the space of positions and directions $\Re^2 \times {\cal S}^1$, where positions are represented using $\Re^2$ and directions using the unit circle ${\cal S}^1$, generates isometric geometrical objects. It has been argued that visual computations occur on $\Re^2 \times {\cal S}^1$, rather than on just $\Re^2$ [1]. The generation of isometries is important for developing a framework for isotropic mappings, as seen later. Isotropic mappings acting on perceptually salient image structures are useful in retrieval, as they illustrate the similarity of different structures in an image. On the other hand, anisotropic mappings indicate the uniqueness of certain attributes of different images.

Most of the previous work in image retrieval has focused on retrieval by image query [2,3,4,5]. However, retrieval by image classification has also gained attention [6,7,8]. In this paper we develop a methodology for retrieval of outdoor images using both image query and image classification by using a nearest neighbor classifier. Retrieval by image query refers to the retrieval of images similar to a given query image from an image database, whereas retrieval by classification refers to the classification of images into certain known classes for retrieval.

As seen in the next sections, perceptual grouping is a natural candidate for isotropic mappings, as are histograms of pixel color values. On the other hand, lower-level texture analysis via a Gabor filter bank (which possesses affinity for certain preferred directions) operating in a channel energy model is an effective candidate for anisotropic mappings.