Image Feature Extraction And Fractality Evaluation Based On Two-Dimensional Continuous Wavelet Transform: Application To Digital Elevation Model Data

A new method to extract image features and to evaluate fractality is proposed based on two-dimensional (2D) continuous wavelet transform (CWT). Multi-directional 2D CWT coefficients are used to determine the direction and magnitude of image intensity gradients directly unlike other methods using gradient components in the horizontal and vertical directions. Image feature points are detected by comparing candidate directional 2D CWT coefficients at candidate points and their neighbors instead of gradient magnitudes or 2D CWT moduli used by traditional methods. It enables us to extract multiscale image features including line singularities such as corners which are recognized to be hardly extracted by traditional methods. This offers an advantage condition to study fractal objects consisting of lots of line singularities. It is suggested that the detected multiscale image features can reflect multiscale fractal measures to be used to evaluate fractality, that is, self-similarity across scales. From this suggestion, the method to evaluate fractality and calculate fractal dimensions using multiscale image features is proposed. The proposed method is applied to theoretical fractal models to show that the method is convenient and effective in extracting image features of them consisting of many line singularities and calculating their fractal dimensions. Finally, the method is validated using a case study dealing with fractality evaluation of geoscientific objects such as coastlines and stream networks from the digital elevation model (DEM) data.