To extract RBT textures, a program called BALL was written in the Microvax -4000 workstation. As our texture of interest was the land use categorical classes known to have varying degrees of variations among them, hence, various ball sizes were initially examined. Only four ball diameters (2,5,7 and 10) were found from visual analysis to have any significant delineation's among land use classes. Hence, these four ball diameters were chosen for extracting full texture of both study areas Plate 1(a) shows an example of textural output of RBT from 512x512 extract of band 5 of a test area using size 5. The smooth component of the RBT textural output for each ball diameter used was then further examined for their effectiveness in the classification of land use.
Figure 1: Schematic representation of the rolling ball transformation. The image form each spectral band is viewed as boxels. In the transformation process, the opening glides the ball on umbra, and closingglides the ball under the umbra following the background contours but does not penetrate the spike A or dimple B (modified after Strenberg 1986).
3.The Ripping Membrane (RM)
The RM was originally proposed by Blake and Zisserman (1987) as an algorithm for solving problem of finding discontinuities (edges) within an image. Unlike many methods of finding discontinuities such as Kernal high pass filter; the RM constitutes a powerful filter, able to detect even weak discontinuities and to localise them accurately with stability. As outlined by the concept of spectral signatures, each individual spectral class can be itemised by a unique spectral vector or digital number (DN) value and abrupt changes in the DN indicated a different type of class. In natural conditions due to the variations in nature (i.e. inherent spatial information), there will be clouds of points emanating from each class. Hence, in finding the vector to represent the class and to localise them have not proven to be simple problem with many kernel filter.
The RM employs the relaxation technique and is based on the analogy with a continuous elastic sheet which is capable, when stretched sufficiently, of ripping. The image is viewed as topography, the x and co-ordinates form the row and column number, while the DN values are the heights of the surface. Blake and Zisserman (1987) orginialy imagined this as an energy function. At each point ina given iamge, a spring is enchored to the height of the image on one end, while the other end is attached to the elastic sheet (Figure 2).
Figure 2: The ripingmembrane illustrated in 1-D. The A,B,C and D are pixel intensities, where the heights are directly proportional to theintensity vectors. The attaching springs are anchored to these points and the other spring -ends are attached to the elastic membrane (after Hashim, 1995)
The shape of the membrane at equilibrium will depend on the relative strength of spring traction and the elasticity of the membrane. Using the concept that a system at equilibrium will have minimum energy, then it is possible to calculate the equilibrium position of the membrane. Hence, the position of the membrane at equilibrium gives the estimation of smooth texture. It is however, possible to overstitch the membrane, as in the case where abrupt changes occurred (i.e. the interface of land and water), and at these junctions the membrane is allowed to rip (thereby reducing the energy).
Mathematically, the solution of such problem is complex. In general form, it the energy E needed for entire spring -membrane system at equilibrium over an interval of x where x [0,n] is given by Blake and Zisserman (1987) as:
E = D + S + P (3)
Where
P is the sum of penalities a accounted for every discontinuity; and
U is the position of the membrane.
Blake and Zisserman (1987) have proposed a solution depending on three factors; (I) how closely the membrane follows the original data (depends on strength of the spring). (2) the elasticity of the membrane (this indicates how well the membrane follows the local smooth average, and ignores individual departures); and (3) the ripping point where the membrane rips (this is where the contextual average can abruptly change). Various solutions can be found by varying these factors. In fact, solutions can be continuously varied from one that closely follows the intensity vectors, to one which follows the large scale average of the intensity vectors.
As the interest in this study lies in the detection of discontinuities that localize class regions, the ripping conditions in intensity were kept fixed, and the relative strength of the springs and the membrane elasticity were varied. Thus, only one parameter, referred to as the range was varied in this study. A large range gives more stiffness to the membrane over the strength of the spring, hence, the solution reflects the contextual average. Similarly, a smaller range will give a solution which fellows more closely the intensity vectors. Subtracting the resultant solutions of the membrane from the original image gives the image portraying the local variations, where the size of the local variations are determined by the chosen range. The smooth solutions, are, however, the main concern in this study. The main inanition is to use RM as a means for estimating the minimized variations caused by spatial information.
In implementing the RM technique, a program based on Graduated Non-Convexity algorithm (GNC) was the Microvax-4000 image processing system. The parameter range that best represented the overall textures was investigated. The range parameters of ,5,7,10,30 and 40 (in unit pixels) were tested in this study. For every range, all the TM band were independently processed with the RM transformation. In effort, the RM technique, replaced the DN value of a pixel by a value which was proportionally closer to the average of DN value of its replaced the DN value of a pixel by a value which was proportionally closer to the average of DN value of its neighborhood. If a difference was larger than the range value (which acts as a threshold), the original DN value was left unaltered. The process was iterated until no pixel in the image changes value (i.e. converges). The smoothed RM values of the corresponding features were then incorporated into the classification process. Visual examples of RM solution using ranges 5,10 and 20 are shown in plate 1(b).
