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Image reconstruction and boundary detection using weak continuity constraints

Sadiye Fatma Guler, University of Massachusetts Amherst


In this dissertation we study the problem of boundary detection and discontinuity preserving reconstruction for a wide class of images. Our objective is to combine these two problems into a single optimization problem and devise an efficient algorithm for its solution. To achieve this goal, we propose a deformable weak-elastic model, namely deformable-membrane model, and the Constrained Graduated Non-Convexity algorithm. Our model preserves the discontinuities and incorporates prior knowledge about the expected shape of the boundaries into the reconstruction process to organize the detected discontinuities. The weak-elastic models used for image reconstruction are based on the weak continuity constraints that model the image discontinuities implicitly. The implicit representation of the discontinuities while giving rise to effective deterministic algorithms, does not allow for including prior knowledge about the geometry of the boundaries detected. On the other hand, boundary detection algorithms need prior knowledge about the image discontinuities to produce smooth and connected boundaries. We incorporate boundary-context information into weak-elastic models, as constraints on an auxiliary line process, by using a set of line configuration constraints. The set of line configuration constraints are assigned favorability coefficients to impose prior knowledge about the boundaries. To preserve the implicit nature of the line process, we translate the constraints on the line process into constraints on the image field. We extend the weak-elastic models to the problem of detecting boundaries in textured images. We use the sufficient statistics of a first-order GMRF model as the image features to represent textured images. Using interacting layers of the deformable-membrane model for image features, the discontinuities detected on each layer are fused to obtain the resultant boundaries. This model allows for the image features to vary slowly within regions, under the weak continuity constraints, corresponding to the nonstationarity of the texture model. The discontinuities are defined as the places where one or more of the image features vary abruptly. We devise an adaptive feature selection criterion to optimally integrate multiple feature data. Based on the observation that the image features may have varying discriminatory properties over the regions of an image, we establish a criterion that employs a measure of between-region variance of image features. We pose the boundary detection and image reconstruction problem as finding the minimum energy state of the deformable-membrane. The energy of the deformable-membrane is a nonconvex function. The prior knowledge about the boundaries introduce constraints into the calculation of the minimum energy state, resulting in a constrained optimization problem. We adopt the Graduated Non-Convexity algorithm and extend it to constrained optimization. We show that a constrained minimum exists, if the line configuration constraints are gradually introduced into the reconstruction process. We develop versions of the algorithm for boundary detection and image reconstruction in intensity images, boundary detection in textured images, and image reconstruction from sparse data and test them on a wide range of synthetic and real images. We also present a survey of the commonly used model-based methods for the low-level image reconstruction problem.

Subject Area

Electrical engineering|Computer science

Recommended Citation

Guler, Sadiye Fatma, "Image reconstruction and boundary detection using weak continuity constraints" (1996). Doctoral Dissertations Available from Proquest. AAI9709601.