Fringe detection in noisy complex interferograms.

A new algorithm to estimate the two-dimensional local frequencies of phase interferometric data is described. With a complex sine-wave model, demonstration is given that a conventional multiple-signal classification (MUSIC) algorithm can be used in spite of multiplicative noise perturbations. A faster algorithm dedicated to the processing of interferograms is developed and a measure of confidence in the estimate is proposed. We studied numerical performances using synthetic fringes. As a result of the frequency estimation, knowledge of the fringe local width and orientation can be applied to restore noisy phase data. Results of a complex phase filter are presented for real interferograms obtained from synthetic aperture radar images.

A 3D reconstruction of vascular structures from two X-ray angiograms using an adapted simulated annealing algorithm.

A three-dimensional (3D) reconstruction of the vessel lumen from two angiographic views, based on the reconstruction of a series of cross-sections, is proposed. Assuming uniform mixing of contrast medium and background subtraction, the cross-section of each vessel is reconstructed through a binary representation. A priori information about both the slice to be reconstructed and the relationships between adjacent slices are incorporated to lessen ambiguities on the reconstruction. Taking into account the knowledge of normal vessel geometry, an initial solution of each slice is created using an elliptic model-based method. This initial solution is then deformed to be made consistent with projection data while being constrained into a connected realistic shape. For that purpose, properties on the expected optimal solution are described through a Markov random field. To find an optimal solution, a specific optimization algorithm based on simulated annealing is used. The method performs well both on single vessels and on branching vessels possessing an additional inherent ambiguity when viewed at oblique angles. Results on 2D slice independent reconstruction and 3D reconstruction of a stack of spatially continuous 2D slices are presented for single vessels and bifurcations.

Contribution to the prediction of performances of the hough transform.

Exact predictions of the performances of the Hough detection of straight lines in two-dimensional images are presented for rectangular and circular retinas, in Cartesian and normal parameterization, in the case of noisy signals. Detection of circles, under the same assumptions, is discussed. The limits of adaptive quantization to reduce intrinsic noise are presented, and it is shown that a signal processing approach is especially convenient to measure the performances of a detector based on the Hough transform.