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Fuzzy Algorithm for 3d Bathymetry Simulation from Topsar Polarised Data
Maged Marghany and Mohd. Lokman Hussien University College Science and Technology Malaysia Institute of Oceanography(INOS) 21030 Mengabang Telipot, Kuala Terengganu Malaysia Email: magedupm@hotmail.com, mmm@kustem.edu.my Introduction The coastal waters bathymetries contemplate as key parameters for coastal engineering and coastal navigation. The bathymetry information is precious for economic activities, for security and for marine environmental protection. Ship borne echo sounder, single-or multi-beam were the classical methods, which utilized to map the sea bottom topography (Hesselmans, 2000). Although these classical techniques provide high precision results, they are very costly and time overwhelming especially when large areas are mapped. Remote sensing methods in real time could be a major tool for bathymetry mapping which they produce a synoptic impression over large areas at comparatively low cost. The airborne Topographic Synthetic Aperture Radar (TOPSAR) contains a wealth information which can be sued to obtain information of the coastal bathymetry. The Jet Propulsion Laboratory (JPL) airborne Topographic Synthetic Aperture Radar (TOPSAR) data were acquired on December 6, 1996 over the coastline of Kuala Terengganu, Malaysia between 103° 5’E to 103° 9’E and 5° 20’N to 5° 27’N. TOPSAR is a NASA/JPL multi-frequency instrument package aboard a DC-8 aircraft and operated by NASA’s Ames research Center at Moffett Field. The TOPSAR system is designed to be flown on small and large aircraft. The system requires a scanner port (18x36 cm) on aircraft underside. TOPSAR is achieved by alternately transmission the signals using horizontal and vertical polarizations. TOPSAR data are operated with fully polarimetric data were acquired at HH-, VV-, HV- and VH-polarized signals from 5x5 m pixels were recorded for three wavelengths: C band (5 cm), L band (24 cm) and P band (68 cm) (Zebker, 1992). The main objective of this study is to develop a geomatic system tool for 3-D bathymetry reconstruction. Model It is generally accepted that the imaging mechanisms of the under water bottom topography is function of the current gradient over the bottom topography. It may be can be explained as (1) interaction between tidal flow and bottom topography leads to modulations in the surface current velocity, (2) modulations in the surface current velocity induce rise to local variations in the wave spectrum and (3) variations in the wave spectrum cause modulations in the radar backscatter (Alpers and Hennings, 1984). A Volterra model was used as nonlinear model to estimate the current gradient from TOPSAR data as follows 
A nonlinear system of equations U(x) = 0, with U:Ân® Ân , is called a block bordered system if it can be written as 
The Fuzzy B-splines Method The fuzzy B-splines (FBS) are introduced allowing fuzzy numbers instead of intervals in the definition of the B-splines. A fuzzy number is defined using interval analysis. There are two basic notions that we combine together: confidence interval and presumption level. A confidence interval is a real values interval which provides the sharpest enclosing range for current gradient values. A assumption level m -level is an estimated truth value in the [0,1] interval on our knowledge level of gradient current Anile (1997). The 0 value corresponds to minimum knowledge of gradient current, and 1 to the maximum gradient current. A fuzzy number is then prearranged in confidence interval set, each one related to a assumption level m Î [0,1]. Moreover, the following must hold for each pair of confidence interval which define a number: m f m¢ Þ Uf U' Let us consider a function ¦: U ® U , of N fuzzy variables u1, u2, ...., un . Where un are the global minimum and maximum values gradient current of the function on the space. Based on the spatial variation of gradient current, algorithms are used to compute the function ¦. The construction begins with the same pre-processing aimed at the reduction of measured current values into a uniformly spaced grid of cells. As in Volettra model data are derived from the LHH TOPSAR backscatter image due to the application of 2-DFFT. First of all, each estimated current data along fix window size of 512x 512 pixels and lines, is considered as a triangular fuzzy number defined by a minimum, maximum and measured value. Among all the fuzzy numbers falling within a window size, a fuzzy number is defined whose range is given by the minimum and maximum values of gradient current along each window size. Among all the intervals extremes, and whose central value is chosen as the "best choice" proficient considering the density of data within window size. Then, a membership function is defined for each pixel element which incorporates the degrees of certainty of radar cross backscatter .
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