#### Technical Report USC-IPI-1055

“Stochastic Singular Value Decomposition Texture Measurement for Image Classification”

by Behnam Ashjari

February 1982

The purpose is to develop an accurate technique for texture feature extraction with low computationality requirements. The particular application explored is image classification. Other possible applications include fast texture segmentation and detection of foreign texture in a textural background.

The singular value decomposition (SVD), a technique of unitary matrix transformation, has been used for extracting features from a texture field. From a large (512 x 512) texture field with correlated pixels, small non-overlapping 32 x 32 sample matrices (texture windows) are randomly selected. Upon SVD transformation on each sample window, a set of 32 singular values are obtained. The singular values contain much of the information regarding correlation contents of matrix elements and their interrelationships. In reality, the SVD reduces two-dimensional processing to one-dimensional, resulting in a substantial saving in computation. Feature selection is performed on the vector of singular values to further reduce its dimensionality to four or less. The reduced dimensional vectors are then used for image classification.

The singular value decomposition is utilized in a stochastic context and the problem of textural feature extraction is approached from a statistical point of view. A connected theory based on stochastic SVD is developed for deriving probability functions of a bidirectionally correlated texture field and probability functions of its singular values.

A family of SVD textural features is introduced. The featuresPI performance is evaluated, individually and in various combinatorial forms, in terms of their strength in texture classification. The classifier is Bayesian and its error criterion is the Bhattacharyya distance (B-distance) measure.

Experiments are performed on two types of textures: artificial and natural. For the first type, bidirectional correlated artificial (computer generated) textures are used. This set of experiments provides an evaluation for the SVD features in a controlled environment. For the second type, four natural textures are used, grass, raffia, sand, and wool. The SVD features B-distance figure of merit classify all of the textures with low probability of error. Computational requirements are also low.

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