Feature Extraction from Wavelet Coefficients for Pattern Recognition Tasks Rajat Aggarwal Chandu Sharvani Koteru Gopinath
Introduction A new efficient feature extraction method based on the fast wavelet transform is presented. The wavelet coefficients from the matrix of each frequency channel are segregated into non-overlapping clusters in an unsupervised mode using a set of application- specific representative image. The proposed method divides the matrices of computed wavelet coefficients into disjoint clusters that are centered around the position of dominant coefficients. The features that can distinguish images of one class from those of other classes are obtained by computing energies of the clusters. The feature vectors so obtained are then presented as input patterns to an image classifier, such as a neural network.
PROCEDURE 1.Binary matrices for cluster determination: The complete 2D discrete wavelet transform is computed for all K represenative images. The following matrices are computed Then we construct the matrices and expect elements of each matrix to be a normal distribution, N(0,1).
We then apply a threshold of the form where (e is euler s number) is the number of computed detail coefficients at each scale to the elements of the matrices G, to get corresponding binary matrices where =1 for x>0 and =0 for x<0. We get binary images B which are passed through a clustering procedure to form boundaries of the clusters.
2. Cluster boundary formation: Step1: Label each occurrence of 1 in the binary matrix with a unique label. Step2: Use these labels and expand by one cell to the left,right,top and bottom. Expansion in any direction is carried out only if neighboring cell is 0, no expansion is carried out if the cell is either a boundary or if neighboring cell is already labelled. Step3: Repeat the same growth pattern of labels until matrix has no more 0. Step4: Once all the 0 in the matrix are labeled cluster boundaries are drawn respecting the homogeneity of the labels in each cluster. In other words, the boundaries are drawn at the interface of differently labeled clusters.
3.Feature extraction method: Now, we have the boundaries of the clusters U1,U2.Uc. From these clusters, the image features u1,u2,u3 uc are determined by simply computing the Euclidean norm of the clusters Each feature ui is determined as the square root of the energy of the wavelet coefficients cluster Ui. Number of features = Number of clusters
Texture Classification The 12 textures(from Brodatz album) are equalized to 256x256 pixels and 256 gray levels. Each image is divided into 16 disjoint 64x64 blocks, and each block is independently histogram equalized to abolish luminance differences among textures. Each original texture block is transformed into one additional block, a 64x64 scaled block obtained from the forty five in the middle.
Texture features and classification Two sets of features,one based on the new clustering scheme and other based on DWT are extracted using the Haar wavelet transform at the maximum decomposition scale J=6. The texture images meant for training the neural networks are used to determine the cluster boundaries to form features u1,u2 uc. Here we have 28 clusters,so we get 28 features. We call this set F1. Using traditional DWT we obtain 19 features that are computed by taking square roots of the energy contents of the DWT. We call this F2. The evaluation of the classification accuracy based on proposed clustering scheme and standard DWT feature extraction method are compared.
Conclusion A new clustering scheme based on 2D wavelet transform is presented, which especially deals with the classification problems using the features extracted from the wavelet coefficients of the images. The results of texture classification have shown that proposed method can efficiently extract most of the problem specific information content intrinsic in input images.
Thank you