The histogram of image intensities is used extensively for recognition and for retrieval of images and video from visual databases. A single image histogram, however, suffers from the inability to encode spatial image variation. An obvious way to extend this feature is to compute the histograms of multiple resolutions of an image to form a multiresolution histogram. The multiresolution histogram shares many desirable properties with the plain histogram including that they are both fast to compute, space efficient, invariant to rigid motions, and robust to noise. In addition, the multiresolution histogram directly encodes spatial information. We describe a simple yet novel matching algorithm based on the multiresolution histogram that uses the differences between histograms of consecutive image resolutions. We evaluate it against five widely used image features. We show that with our simple feature we achieve or exceed the performance obtained with more complicated features. Further, we show our algorithm to be the most efficient and robust.

Intensity histograms have been used extensively for recognition and for retrieval of images and video from visual databases. Intensity histograms of images at different individual resolutions have also been used for indexing. They suffer, however, from the inability to encode spatial image information. Spatial information can be incorporated into histograms simply by taking histograms of an image at multiple resolutions together to form a multiresolution histogram. Multiresolution histograms can also be computed, stored, and matched efficiently. The authors analyze and quantify the relation and sensitivity of the multiresolution histogram to spatial image information as well as to properties of shapes and textures in an image. They verify the analytical results experimentally and demonstrate the ability of multiresolution histograms to discriminate between images, as well as their robustness to noise.

Histograms are used to analyze and classify images. They have been found experimentally to have low sensitivity to certain types of image morphisms, for example, viewpoint changes and object deformations. However the precise effect of these image morphisms on the histogram has not been studied. In this work we derive the complete class of local transformations that preserve the histogram or simply scale its magnitude. To achieve this the transformations are represented as solutions to families of vector fields acting on the image. It is then shown that weak perspective projection and paraperspective projection belong to this class and simply scale the histogram. The results on weak perspective projection, together with the effect of illumination, are used to compute the histogram of the projection of 3D polyhedral objects. We verify the analytical results with several examples. Moreover we present and test a system that recognizes and approximates the poses of 3D polyhedral objects independent of viewpoint.