Histograms: Properties and Applications

Histograms have been used extensively for recognition and retrieval of images and videos from visual databases. They are efficient and have been found to be robust to certain types of image morphisms, such as small viewpoint changes and object deformations. The precise effect of these image morphisms on the histogram has not been studied in the past. In the first part of this project, we have derived the complete class of continuous image transformations for which the histogram is invariant. These transformations are relevant to any histogram-based image recognition system. We have also showed that polyhedral objects with unknown poses can be recognized based on the histograms of their faces.

In the second part of the project, we have developed a multiresolution histogram representation and used it in recognition applications. It is well-known that a single histogram of an image does not encode spatial image variations. Spatial information can be captured by computing histograms for multiple scales (resolutions) of the image. In our specific representation, we compute the differences between the intensity histograms of consecutive image resolutions and simply concatenate these differences to form a feature that we refer to as the multiresolution histogram. We have shown that the multiresolution histogram captures important information about shapes and textures in images. The multiresolution histogram, like the single histogram, can be computed, stored and matched very efficiently. The ability of multiresolution histograms to discriminate between images of different classes is demonstrated using databases of synthetic as well as real images.

Publications

"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] [©]

"Spatial Information in Multi-resolution 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] [©]

"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] [©]

"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] [©]

Images

  Histogram Preserving Image Transformations:

The top-left image is transformed with Hamiltonian transformations to produce the remaining three images. These images are severely distorted and yet have exactly the same histogram as the original image. The histogram of an image is invariant if and only if the image is transformed with a Hamiltonian transformation.

     
  Pose Estimation of Polyhedral Objects:

The class of histogram preserving image transformations has been used to identify image projection models that preserve the histogram (up to a scale). The projections include the weak-perspective and para-perspective projections. Based on this observation, the histogram of a polyhedral object can be expressed as the sum of the histograms of the projections of its visible faces. This representation can be used to estimate the pose of a polyhedral object.

     
  Effect of Shape on the Multiresolution Histogram:

The images on the left are parameterized superquadrics. Their histograms are approximately the same. The plot shows the rate of change of the histogram with image resolution plotted as a function of the superquadric parameter. The rate of change is minimum for a circle and increases for shapes with sharp corners.

     
  Effect of Texture on the Multiresolution Histogram:

The images on 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 plotted as a function of the randomness of the texel placement. The rate of histogram change decreases with the randomness.

     
  Texture Recognition Using Multiresolution Histograms:

Several textures from the Brodatz database under different rotations are seen in this picture. The multiresolution histogram was used to match textures. Matching works well because the multiresolution histogram captures spatial information and at the same time is invariant to rotations of the image.

     
  Texture Recognition under Illumination and Viewpoint Changes:

The CURET database includes 3D textures imaged from different viewpoints and under different illuminations. The multiresolution histogram was used to match different instances of these textures. This experiment demonstrates that the multiresolution histogram is robust to illumination and viewpoint changes as well.

     

Database

CURET: Reflectance and Texture Database

Appearance Matching