Decomposition of stochastic properties within images using non-parametric methods

This paper discusses the application of three different nonparametric methods for decomposing images into regions which exhibit special stochashc es, together with the statistics in connection With steps in the emplrical estimated distribution functions; 2) detection of stochastic informahon wi image by hypothesis testing; 3) rank order stahstics to ose the different types of stochastic mthin an mage The decomposition is used to isolate different mage regions and to estimate the proc hich are the constituent stochastic components. In or hieve this, decisions based upon membership relations are employed and adapted sed. The thresholds are obtained by the ordering of terms calculated by stochastic estimation methods together forementioned techniques. The decomposition of images into separate parts with different stochastic properties is obtained by calculating selected portions of the distribution function, using ordering of statistics. The ordering uses a specific set of grey values of pixel elements in the image. For such an ordering set an empirical integral function of the distribution [l] is calculated, by summation of step functions with selected thresholds within a stochastic region. These overlaid stochastic processes are described by using the difference and the height of the levels of the pre-processed integral distribution function. These levels are estimated by analysis of the stochastic empirical properties. The non-parametric method of ordering allows a soft decision to be made in classifying the membership set of pixel values, to a selected stochastic property. University of Glamorgan, Dept. of Electronics (42 IT, E-Mail: lsdooley@glam ac uk Awledge concerning ble stochastic properties within regions of the image, can be identified by testing assumptions. The test provides a value that represents the similarity between the stochastic property in a selected region with one of the assumed a priori properties. The set of elements of the selected region is give Where 1 = k + r and the distribution function (DE) of the selected region with 1 other neighbouring elements written as:l P P r= i fqx, Xrei)=Cub X p r e y ( 9 Where p is the number of grey levels xgrey that occurs in the I elements and U is the unit step function. A threshold can then be calculated to decide upon the degree of similarity. Ordering of the DF does not afford the possibility to detect shifting areas, while the correlation between regions'does. Another description of the stochastic may be obtained by the ordering of a special sub-region s with elementsx, . Such ordering in v sub-regions can be expressed as:1 ' F, k = l {U(., -U(X X ( k ) ) ] A simple example of which would be where the values X, are obtained by setting a minimal threshold, and then summing Over a special area. This is identical to the bitimage of the least significant bits.