Rotation invariant perimeter and invariant compactness for texture elements

Structural properties of texture elements in a surface have successfully been applied to characterise textures. For this purpose, histograms of texture element's properties are used. Compactness property of an element has been used for characterisation. The compactness depends upon its perimeter. A novel method based on perimeter contribution, to compute the value of perimeter is presented. The perimeter value computed using the proposed method is closer to the actual, than the perimeter value computed using the conventional methods. The value of perimeter using proposed method is also more consistent than the conventional methods. The value of compactness using the proposed method are not only closer to actual value but also more consistent under affine transformations. Invariant histogram of compactness using the invariant value of compactness characterises texture invariant of scaling and rotation.<>