The Beauty Farm A Wavelet Method for Edge Preserving Piece-wise Smooth Approximations of Radar Images

• Published in: Spatial Analysis for Radar Remote Sensing of Tropical Forests Vol. 1; pp. 237 - 254
• Main Authors: De Grandi, Gianfranco (Frank), De Grandi, Elsa Carla
• Format: Book Chapter
• Language: English
• Published: CRC Press 2021
• Edition: 1
• Subjects: SAR Data; Original SAR Image; Wavelet Coefficients; Kappa Analysis; TRFIC; Object Based Change Detection; Wavelet Method; Inverse Wavelet Transform; Wavelet Variance; Real SAR Data; Wavelet Transform; SAR Image; SAR Backscatter; PALSAR Image; Maxima Trajectory; InSAR Coherence; ISODATA Algorithm; Gradient Modulus; Wavelet Maxima; InSAR Observation; Error Matrices; Discrete Wavelet Transform; Real SAR Image; Speckle Noise
• ISBN: 0367259400; 9780367742669; 0367742667; 9780367259402
• DOI: 10.1201/9780429290657-10

Many high-performance segmentation and classification algorithms are designed with a specific class of imagery in mind, namely optical images (with additive noise) including objects with smooth surfaces. They are therefore ill-suited to deal with radar images because of speckle noise and textured classes. An approach is presented in this chapter to make the radar images fit the requirements of those clustering algorithms that take advantage of a consolidated theory and validated performance. The goal is achieved by the combination of a proper image model, the discrete wavelet transform, and the connection with the Lipschitz regularity (see Chapter 7). The image model comprises scenes with areas of interest defined by strong transitions at their contour (called stitches) and transitions within the area caused by noise. Imagining moving the scene on to a large scale (e.g. by a wavelet transform): the image will become increasingly smooth, stitches belonging to variations within the area (caused by noise and texture) will fade away, while the ones belonging to the contour of the area will persist. This is because the "type" of discontinuity caused by noise is different from the type related to the edge - in the first case it is like a spike, and in the second it is a step (see also Chapter 7). Reversing the move from large scale to short scale and keeping only the stitches belonging to contours of the areas of interest will perform the trick of generating a piece-wise smooth radar image, yet preserving the important contours. This sleight of hand is possible through an image reconstruction algorithm based on the inverse wavelet frame transform and exploiting the evolution with scale of wavelet modulus local maxima detected scale-by-scale by a maxima tracking algorithm. The algorithm is described in detail using a programming pseudo-language notation. Problems related to speckle noise and textural edges are discussed. Importantly, a bespoke region growing classifier was implemented that exploits information from local statistic (mean and variance) of the smooth image (i.e. estimated in the neighborhood of a point in the field) and from the chained maxima (edges) supplied by the smooth image generator. A practical implementation of the algorithm is described, concerning a mapping experiment aiming at land cover mapping over large areas of South American tropical regions using the SAR mosaics developed within the GRFM initiative. Processing methods and selected results are presented. The mapping exercise included three test sites in South America (Mato Grosso, Rondônia and Colombia), each presenting different ecological content of the Amazon landscape. Validation of the radar maps was undertaken using forest thematic maps derived from LANDSAT imagery by the NASA Tropical Rain Forest Information Centre (TRFIC). Validation results are reported in terms of overall accuracy for the thematic subset forest/non-forest and the SAR data processed by the wavelet method and a region growing classifier resulting in 91%, 73%, and 57% accuracy for the Mato Grosso, Rondônia and Colombia sites, respectively. Kappa analysis was performed to assess the agreement of the GRFM maps with reference data and the significance of the difference between maps generated using the wavelet smooth approximation and the ISODATA algorithm with the original speckled SAR data. This analysis indicated that maps derived by the wavelet method were always more accurate than maps derived by ISODATA and the original GRFM datasets. In this chapter, a wavelet method for reconstructing piece-wise smooth approximations of the original synthetic aperture radars (SAR) backscatter image while at the same time preserving discontinuities is presented. A two-dimensional wavelet frame representation, with the mother wavelet acting as a differential operator, is then performed. Next, a more formal description of the flow of operations is provided. Algorithms for the reconstruction of a signal from the extrema of its wavelet transform have been proposed. The analysis shows that speckle noise impacts the reconstruction methods in two ways. A research project aiming at land cover mapping over large areas of the South America tropical regions using the SAR mosaics developed within the Global Rain Forest Mapping (GRFM) initiative is outlined. The main objective of the project was to assess the capability of supporting by means of the GRFM mosaics a regional scale tropical forest mapping exercise in the Amazon.