In this paper, we develop a new unified approach for laser radar range anomaly suppression, range profiling, and segmentation. This approach combines an object-based hybrid scene model for representing the range distribution of the field and a statistical mixture model for the range data measurement noise. The image segmentation problem is formulated as a minimization problem which jointly estimates the target boundary together with the target region range variation and background range variation directly from the noisy and anomaly-filled range data. This formulation allows direct incorporation of prior information concerning the target boundary, target ranges, and background ranges into an optimal reconstruction process. Curve evolution techniques and a generalized expectation-maximization algorithm are jointly employed as an efficient solver for minimizing the objective energy, resulting in a coupled pair of object and intensity optimization tasks. The method directly and optimally extracts the target boundary, avoiding a suboptimal two-step process involving image smoothing followed by boundary extraction. Experiments are presented demonstrating that the proposed approach is robust to anomalous pixels (missing data) and capable of producing accurate estimation of the target boundary and range values from noisy data.

In this paper, we develop a new approach to tomographic reconstruction problems based on geometric curve evolution techniques. We use a small set of texture coefficients to represent the object and background inhomogeneities and a contour to represent the boundary of multiple connected or unconnected objects. Instead of reconstructing pixel values on a fixed rectangular grid, we then find a reconstruction by jointly estimating these unknown contours and texture coefficients of the object and background. By designing a new "tomographic flow", the resulting problem is recast into a curve evolution problem and an efficient algorithm based on level set techniques is developed. The performance of the curve evolution method is demonstrated using examples with noisy limited-view Radon transformed data and noisy ground-penetrating radar data. The reconstruction results and computational cost are compared with those of conventional, pixel-based regularization methods. The results indicate that the curve evolution methods achieve improved shape reconstruction and have potential computation and memory advantages over conventional regularized inversion methods.

In this paper, we develop a new active contour model for image segmentation using adaptive flows. This active contour model can be derived from minimizing a limiting form of the Mumford-Shah functional, where the segmented image is assumed to consist of piecewise constant regions. This paper is an extension of an active contour model developed by Chan-Vese. The segmentation method proposed in this paper adaptively estimates mean intensities for each separated region and uses a single curve to capture multiple regions with different intensities. The class of imagery that our new active model can handle is greater than the bimodal images. In particular, our method segments images with an arbitrary number of intensity levels and separated regions while avoiding the complexity of solving a full Mumford-Shah problem. The adaptive flow developed in this paper is easily formulated and solved using level set methods. We illustrate the performance of our segmentation methods on images generated by different modalities.

In this paper, we develop a new approach to tomographic reconstruction problems based on geometric curve evolution techniques. We use a low order parametric model to describe the shape and texture of the object support as well as the background. This model uses a set of texture coefficients to represent the object and background inhomogeneities and a contour to represent the boundary of multiple connected or unconnected objects. The problem of determining the unknown contour and texture coefficients of the object and background medium is then formulated as a non-linear estimation problem. By designing a new, "tomographic flow", the resulting problem is recast into a curve evolution problem and an efficient algorithm based on level set techniques is developed. The performance of the curve evolution method is demonstrated using examples with noisy Radon transformed data and noisy ground penetrating radar data. The reconstruction results and computational cost are compared with those of conventional regularization methods. The results indicate that our curve evolution methods achieve improved shape reconstruction with reduced computation requirements.

We develop a statistical approach for imaging weak-contrast objects buried under a rough soil/air interface using data from a ground penetrating radar array. The imaging system uses short-pulse electromagnetic plane waves as illumination signals. We develop an approximate physical model based on a flat soil/air interface and weak-scattering to relate the collected data to the buried objects. This model uses ray optics to represent the soil/air interface, and a Born approximation to model the weak contrast backscattering from the buried objects. In order to form images of objects buried under rough soil/air interfaces, we embed our model in a statistical framework to account for modeling errors and ill-posedness. The statistical framework leads to optimal reconstruction algorithms for buried objects. We evaluate the performance of the reconstruction algorithms for different soil/air interface realizations using data generated from detailed nonlinear electromagnetic simulations of ground penetrating radar.

We develop a new geometric curve evolution approach to tomographic reconstruction problems including multiple objects having different levels of intensity, and background with varying intensity. We use two contours to represent the boundaries of distinct object regions with different intensity levels and a set of basis functions and expansion coefficients to describe the background. By designing coupled "tomographic flows", the problem of estimating the two contours and intensity coefficients is recast into a curve evolution problem. A new "repelling" force between the two coupled curves is proposed for the reconstruction algorithms to accelerate convergence. The performance of the coupled curve evolution method is demonstrated via a Radon inversion example. The results show that our curve evolution method achieves improved shape reconstruction over comparable regularization techniques.