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Wavelet based Texture Analysis

Our interest lies in studying the problem of finding optimal wavelet representations for both periodic and granular types of texture. Wavelet packets are well-known for their ability to compactly represent textures consiting of oscillatory patterns such as fingerprints or striped cloth. The discrimination power of a wavelet packet subband can be defined as its ability to differentiate between any two texture classes in the transform domain, consequently leading to better classification results. The problem of adaptive wavelet basis selection for texture analysis can, therefore, be solved by using a dynamic programming approach to find the best basis from a library of orthonormal basis functions with respect to a discriminant measure. Our WaveletsX'2003 paper presented a fast basis selection algorithm which extended the concept of 'Local Discrminant Basis' (Saito and Coifman, 1994) to two dimensions. It was shown that wavelet packets are good at representing not only oscillatory patterns but also granular textures. Comparative results were presented for four different distance metrics: Kullback-Leibler (KL) divergence, Jensen-Shannon (JS) divergence, Euclidean distance, and Hellinger distance. It was also shown that combining the two approaches offers a significant advantage over other feature selection methods in that both basis selection and reduction of dimensionality of the feature space can be done simultaneously.

Recently, we have also applied these ideas to the classification of meningioma images.

 

Optimal WP basis with best 4 subbands selected
Segmentation results with only 4 selected WP features

The computational complexity of a feature-based texture segmentation algorithm is limited by the dimensionality of the feature space. Although finding the optimal feature subset is a NP-hard problem (Boz, 2002), a feature selection algorithm that can reduce the dimensionality of problem is often desirable. The problem of discriminant wavelet packet feature selection was first addressed in the SCAS'2002 paper, whereby the value of a cost function associated with a subband (feature) is used as a measure of relevance of that subband for classification purposes. This leads to a fast feature selection algorithm which ranks the features according to their measure of relevance. In our BMVC'2003 paper, we compared the results of this feature selection algorithm for texture segmentation using two different subband filtering methods: a full wavelet packet decomposition and a Gabor type decomposition. Experiments on a range of test images and both filtering methods provide results that are promising.

 

F17D15er
Segmentation results with only 3 Wavelet features

Texture Segmentation with Ants 

In a separate work presented at ICIP'2006 and ICEIS'2006, a novel texture classification algorithm was proposed which was inspired by the self-assembling behavior of real ants when building live structures with their bodies. The proposed algorithm employs wavelet (ordinary, wavelet packet, or Gabor) filter banks for extracting discriminant features from images containing multiple textures not known to the algorithm. The feature space is clustered using a novel ant tree clustering (ATC) algorithm based on the similarity of ants carrying the feature vectors. The clustering process is motivated by the self-assembling behavior of natural ants for forming mechanical structures such as drops, crossing chains, and building chains. It works by progressively attaching ants to an existing support and then successively to other already attached ants, thus building trees based on the similarity of ants (ie, feature vectors). While being computationally efficient, the probabilistic nature of the algorithm allows it to avoid local minima which the traditional k-means algorithm may get stuck in.

 

Clustering with Ants

 

Relevant Publications

  • A Hussain, NM Rajpoot, KM Rajpoot,
    Texture Classification with Ants,
    in Proceedings IEEE International Conference on Image Processing (ICIP'2006), October 2006
    poster
  • AH Channa, NM Rajpoot, KM Rajpoot,
    Texture Segmentation using Ant Tree Clustering,
    in Proceedings IEEE International Conference on Engineering of Intelligent Systems (ICEIS'2006), April 2006
  • KM Rajpoot, NM Rajpoot,
    Wavelets and Support Vector Machines for Texture Classification,
    in Proceedings 8th IEEE International Multitopic Conference (INMIC'2004), December 2004
  • AH Bhalerao and NM Rajpoot,
    Discriminant Feature Selection for Texture Classification,
    in Proceedings British Machine Vision Conference (BMVC'2003), Norwich (UK), September 2003
  • NM Rajpoot,
    Local Discriminant Wavelet Packet Basis for Texture Classification,
    in Proceedings SPIE Wavelets X (Wavelets X'2003), San Diego (USA), August 2003
  • NM Rajpoot,
    Texture Classification using Discriminant Wavelet Packet Subbands,
    in Proceedings IEEE 45th Midwest Symposium on Circuits and Systems (MWSCAS'2002), August 2002