Transformation invariant features of space curves and its application in classification problems

Abstract

The invariance property of curves under scaling, rotation and translation has been elaborately studied by research fraternity working on four-bar linkage mechanism. In fact, the authors detect that this invariance property will be useful in image classification problems. However, most of the existing works on four-bar linkage problems are associated with planar curves. Contrarily, the classification problems are based on the boundary space curves of the shapes of the images. Further, the strategy to study the invariance property adapted for the planar curve is not suitable for curves in space. Therefore, in our proposed work, the principal components of the sample points of the space curve are obtained, on which the atypical wavelet transform is performed for all the principal components. It is interesting to note that the desired relationship is found to be present in a specific ratio of atypical wavelet detailed coefficients of the points obtained by principal components. It is shown that this ratio, when included as a feature in classification problems enhances efficiency. In this study, we accomplish the classification of images by machine learning using the proposed feature along with the conventionally measured values.

Keywords

• space curves
• sample points
• pca
• atypical wavelet transform
• invariant feature vector
• classification
• machine learning
• measured values