Deterministic and stochastic separation of digital images

Document Type

Article

Publication Date

1-1-1994

Department

Department of Mechanical Engineering-Engineering Mechanics

Abstract

The digital image of a scene is composed of patterned and textured regions, which are separated by boundaries or edges. This paper presents a three stage approach to separating the regions which constitute the structural or deterministic component of the image and the textures which constitute the stochastic part of the image. The data dependent system methodology is extended to the boundary value problem, to achieve time (space) and frequency localization on the image data. The peculiarity of this approach is that it identifies each texture as one entity, as opposed to conventional approaches which give rise to a number of edgelets for each texture in the image. The first stage generates a mathematical characterization of the image using the intrinsic spatial dependencies of the image intensities. The dynamics of the image intensities is characterized by the Green's function of the adequate model. The components of intensities unexplained by the Green's function are captured in the model residuals. These residuals contain both boundary values and noise. Boundary values occur at the outlier residual locations and are nonzero only at the region boundaries. In the second stage a linear regression that minimizes the stochastic part of the model is used to estimate the boundary values, which are measures of edge strength. The third stage involves the deterministic and stochastic reconstruction of the image, which demonstrates the structural and textural separation of the image. Convolution of boundary values with Green's function gives the structural component, whereas convolution of white noise with Green's function produces the textural component of the image. The results show excellent structural textural separation in addition to large data reduction capability.

Publication Title

Journal of Visual Communication and Image Representation

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