Atypical Wavelet Descriptor of Curves Using Principal Components

Abstract

The relationship between the sample points of a space curve and scaled, rotated and translated sample points are often not evident either geometrically or analytically. However the research fraternity working on linkage mechanism found this relationship useful for their study which they captured through Fourier and wavelet transforms. It is significant to observe that most of the research works carried out is pertaining to planar curves. Further the strategy adapted for the planar curve is not suitable for the curves in space. This challenge of extracting relationship between both the sets of sample points of the space curve motivates the authors to suitably reduce the dimension and proceed.  In our proposed work the Principal Component Analysis (PCA) is used to reduce the dimension of the sample points of the space curve to the points on a plane. 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 dimensional reduction. The results are also supported by illustrating examples of continuous curves.