Use of histograms for recognition

Histograms have been used extensively for recognition and for retrieval of images and video from visual databases. They are efficient and have been found experimentally to be robust to certain types of image morphisms, such as viewpoint changes and object deformations. The precise effect of these image morphisms on the histogram has not been studied.; The first topic examined in this work are the transformations that preserve the histogram of any arbitrary image they are applied to. In particular, the complete class of histogram preserving continuous transformations is derived. Several applications of this class of transformations are shown and their significance for histogram based image indexing is discussed.; Individual histograms of images at resolutions lower than that of the original image have also been used for image indexing. A single image histogram, however, suffers from the inability to encode spatial image variation. Spatial variation can be incorporated into histograms simply by taking intensity histograms of an image at multiple resolutions to form a multiresolution histogram. It is shown that for several classes of images the multiresolution histogram depends on parameters and properties of image shapes and textures.; Two characteristics of the multiresolution histograms that significantly affect their indexing performance are examined. The first is the intensity resolution of the histograms. The second is the bin width of the histograms. The bin width can be identical for the histograms of all image resolutions or it can depend on image resolution.; Two different norms are used to compute the distance between multiresolution histograms. For the first norm, the intensity histograms of the various image resolutions are concatenated to form a feature vector. For the second norm, the differences between the intensity histograms of consecutive image resolutions are concatenated to form a feature vector. The distance between the feature vectors for both norms was computed using L₁. Multiresolution histograms, like single histograms, can be computed, stored, and matched efficiently. They also retain the robustness of the plain histograms.; The ability of multiresolution histograms to discriminate between images of different classes is demonstrated experimentally. The experiments are performed using three databases. The first is a database of synthetic images. The second is a database of Brodatz textures [19]. The last database consists of CUReT textures [35]. Multiresolution histograms are shown to be robust to rotations, noise, database size, and intensity resolution.; The performance of the multiresolution histogram as an image feature is compared to that of five other commonly used image features. The five image descriptors are Fourier power spectrum features, Gabor wavelet features, Daubechies wavelet packets energies, auto-cooccurrence matrices, and Markov random field parameters. The multiresolution histogram is found to be very efficient and the most robust feature.; Finally, the Shannon entropy of the multiresolution histograms is used to reveal geometric properties of images. It is also used to select resolutions that increase the discriminability based on histograms between different image classes.