Filter and Filter Bank Design for Image Texture Recognition

Trygve Randen (e-mail:
Submitted in partial fulfillment of the degree Doktor Ingeniør
Stavanger College / Norwegian University of Science and Technology

Defended in Stavanger November 24, 1997

Full thesis can be found here


The focus of this dissertation is on the design of two-dimensional filters for feature extraction, segmentation, and classification of digital images with textural content. The features are extracted by filtering with a linear filter and estimating the local energy of the filter response. The dissertation gives a review covering broadly most previous approaches to texture feature extraction and continues with proposals of several new techniques.

Texture feature extraction using a quadrature mirror filter (QMF) bank is proposed, utilizing both critically sampled and full rate implementations. In the critically sampled case, tremendous computational savings can be realized. One of the major conclusions of the experiments is that it is possible to use sub-sampled filters with only a modest degradation in segmentation accuracy -- realizing considerable computational savings. Furthermore, the commonly used octave band decomposition is evaluated against alternative decompositions, concluding that non-octave decompositions are generally superior. The QMF filter bank features are tested on benchmark images, on document segmentation, and on image content search.

The use of linear least squared prediction error filters is also proposed, yielding an optimal representation of the textures. Compared to non-optimized filter banks, this approach yields a low number of feature images for problems with a moderate number of textures. Still good classification results are obtained in most cases. However, being optimal with respect to texture representation does not guarantee optimality with respect to discrimination. Therefore, approaches for the design of filters with optimal energy separation are proposed. For two-texture problems, an exact closed form solution optimizing the relative distance between the average feature values is derived. Furthermore, an approximate solution for the Fisher criterion is also derived. For both of these solutions, the coefficient vector of the optimal filter is selected from the eigenvectors of the same matrix. A generalized criterion leading to the same eigenproblem is therefore introduced. Motivated by this generalized criterion, a scheme selecting the filter coefficient vector with respect to minimum feature histogram overlap is proposed. The methods are also extended to multiple texture cases and unsupervised problems. A model for the feature extraction process is required for the optimization and is developed and assessed.

The performances of the proposed methods are shown in extensive experiments. These experiments also incorporate methods broadly covering most approaches to texture feature extraction with filters, along with a few non-filtering approaches. The results clearly justify the new approaches.

Finally, new methods for automated seismic interpretation are proposed. In these techniques, the dominating orientation of the seismic is estimated. It is shown that applying filters tuned with respect to the dominating orientation in the seismic signal, powerful features for the detection of discontinuities in the seismic data, i.e., faults, may be extracted. It is furthermore shown how the orientation flow yields tools for analyzing stratum interfaces.