Tree Image Growth Analysis Using the Instantaneous Phase and Frequency Modulation

Abstract

We propose the use of Amplitude-Modulation Frequency-Modulation (AM-FM) methods for tree growth analysis. Tree growth is modeled using phase modulation. For adapting AM-FM methods to different images, we introduce the use of fast filterbank filter coefficient computation based on piecewise linear polynomials and radial frequency magnitude estimation using integer-based Savitzky-Golay filters for derivative estimation. For a wide range of images, a simple filterbank design with only 4 channel filters is used. Filterbank specification is based on two different methods. For each input image, the FM image is estimated using dominant component analysis. A tree growthmodel is developed to characterize and depict quarterly and half-seasonal growth of trees using instantaneous phase. Qualitative evaluation of inter- and intraring reconstruction is performed on 20 aspen images and a mixture of 12 tree images of various types. Qualitative scores indicate that the results were mostly of good to excellent quality (4.4/5.0 and 4.0/5.0 for the two databases, resp.).