Computational Complexity Reduction in Feature Detection via Nonlinear Component Analysis and Information Quantitative Synthesis

Feature detection exemplifies a promising area in digital image processing. Local features manifest the distinct and informative details in sub-images. Global features instead provide holistic aspects across entire digital images. To minimize the information loss, the large memory space and high dimensional data are necessary in image processing. It gives rise to the computational complexity issues. Being the alternative solutions, some computational efficiency enhancement and dimensionality reduction schemes are potentially needed. Principal component analysis (PCA) is traditionally a dominating technique. However, nonlinear component analysis (NCA) will be more powerful to deal with multivariate large dimensional nonlinear problems up to infinite dimensionality. NCA is thus applied for dimensionality reduction in context for feature detection cases covering practical land, sea and space information. The selective set of quantitative metrics based on statistics is well defined and proposed for information quantitative synthesis, including the discrete entropy, relative entropy and mutual information in the frequency domain, together with the dissimilarity, contrast and correlation in the spatial domain in order to ensure the information integrity from diverse aspects. Numerical simulations verify the significance of the NCA approach.