Use of the empirical mode decomposition and hilbert-Huang transform in image analysis

The new method for analyzing nonlinear and nonstationary data described by Huang et al. [1,2] has been expanded to include the analysis of image data. The key steps of this new robust approach have been followed in this extension of the method. The images analyzed here are first decomposed into horizontal strips corresponding to each pixel row. For an image of 512 x 512 pixels, this would mean that a set of 512 slices, each 512 pixels long, would be first obtained. Then the Empirical Mode Decomposition (EMD) method of Huang et al. [1,2] and Huang [3] is applied, resulting in a small number of Intrinsic Mode Functions (IMF) for each image slice. Because the decomposition is based on the local characteristic time scale or length scale of the data, it is applicable to images of nonlinear and nonstationary processes. By next applying the Hilbert transform to the decomposition components of each image slice, the methods yield instantaneous frequencies or wave numbers as functions of time or distance, that give sharp identifications of imbedded structures. Thus for each image slice, we obtain a decomposed component set, ranging from the smallest time or length scales to the largest. The sum of these components is the original starting data. These results can then be used in several important ways. First, the components resulting can be reassembled into component images, by combining the first component from each slice together into a first component image (containing the highest frequencies or shortest length scales), and then repeating this for each subsequent component from each image slice. This gives a set of images that reveal different scales, from shortest to longest. Another presentation is obtained from the Hilbert transforms of the components, which can then be combined into an energy-frequency (or wave number)time distribution. Examples of this extension into images is given for water wave slopes in the presence of opposing current, and in satellite imagery of El Nino effects.