Histograms: Properties and Applications
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. In this work we derive the complete class of histogram preserving continuous image transformations. These transformations are significant for histogram based image indexing. We also showed that polyhedral objects can be recognized based on the histograms of their faces.

Individual histograms of an images or of lower resolutions of an image suffer from the inability to encode spatial image variation. That information can be incorporated into histograms simply by taking intensity histograms of an image at multiple resolutions. In this work the differences between the intensity histograms of consecutive image resolutions are concatenated to form a feature, namely the multiresolution histogram. The appropriate histogram bin width as a function of image resolution is examined. It is also shown that the multiresolution histogram depends on properties of image shapes and textures. 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 using databases of synthetic as well as real images. The entropy of the histograms of the various image resolutions is also examined.

Publications

"Histogram Preserving Image Transformations,"
E. Hadjidemetriou, M.D. Grossberg and S.K. Nayar,
IEEE Conference on Computer Vision and Pattern Recognition (CVPR),
Vol.1, pp.410-416, Jun, 2000.
[PDF] [bib] [©]


"Histogram Preserving Image Transformations,"
E. Hadjidemetriou, M.D. Grossberg and S.K. Nayar,
International Journal on Computer Vision,
Vol.45, No.1, pp.5-23, Oct, 2001.
[PDF] [bib] [©]


"Spatial Information in Multiresolution Histograms,"
E. Hadjidemetriou, M.D. Grossberg and S.K. Nayar,
IEEE Conference on Computer Vision and Pattern Recognition (CVPR),
Vol.I, pp.702-709, Dec, 2001.
[PDF] [bib] [©]


"Multiresolution Histograms and their use for Recognition,"
E. Hadjidemetriou, M.D. Grossberg and S.K. Nayar,
IEEE Transactions on Pattern Analysis and Machine Intelligence,
Vol.26, No.7, pp.831-847, Jul, 2004.
[PDF] [bib] [©]


"Multiresolution Histograms and their use for Texture Classification,"
E. Hadjidemetriou, M.D. Grossberg and S.K. Nayar,
3rd International Workshop on Texture Analysis and Synthesis (Texture 2003),
Oct, 2003.
[PDF] [bib] [©]


"Resolution Selection Using Generalized Entropies of Multiresolution Histograms,"
E. Hadjidemetriou, M.D. Grossberg and S.K. Nayar,
European Conference on Computer Vision (ECCV),
Vol.I, pp.220-235, May, 2002.
[PDF] [bib] [©]


Pictures

   Histogram preserving image transformations:
The image in the top left is transformed with Hamiltonian transformations. The resulting images are severely distorted. However, the histograms of the images are not affected. In fact, the histogram of an image remains invariant if and only if the image is transformed with a Hamiltonian transformation.
  Estimation of the pose of polyhedral objects:
We extended the histogram preserving image transformations to image transformations which scale the histogram. Some of these transformations are the weak-perspective and para-perspective projections. These were applied to the projection of polyhedral objects. The histogram of such an object was expressed as the sum of the histograms of the projections of its visible faces. This allows the estimation of the pose of a polyhedral object.
  Dependence of the multiresolution histogram on shape:
The images in the left are parameterized superquadrics. Their histograms are approximately the same. The plot shows the rate of change of the histogram with image resolution w.r.t. superquadric parameter. The rate of change is minimum for a circle and is increased for shapes with sharp corners.
  Dependence of the multiresolution histogram on texture:
The images in the left are textures with texels placed with an increasing degree of randomness. Their histograms are approximately the same. The plot shows the rate of change of the histogram with image resolution w.r.t. the randomness in texel placement. The rate of histogram change decreases with randomness.
  Database indexing with the multiresolution histogram:
Several textures from the brodatz database under different rotations. The multiresolution histogram was used to match different rotation instances of the same texture. This demonstrates that the multiresolution histogram in addition to being able to represent spatial image information, is also rotationally invariant.
  Database indexing with the multiresolution histogram:
The images in the CUReT database show physical textures imaged from different viewpoints and under different illuminations. The multiresolution histogram was used to accurately match different instances of these textures. This demonstrates that the multiresolution histogram is robust to illumination and viewpoint changes.
  Entropies of multiresolution histograms:
The image of a fingerprint together with a plot of the Shannon entropy values of its multiresolution histograms. The plot scales linearly with object size. Thus, it allows the comparison of the multiresolution histograms of objects imaged in different resolutions.

Related Projects

CURET: Reflectance and Texture Database

Appearance Matching