Finding sparse parametric shapes from low number of imase measurements

Detection of parametric shapes i.e. line, circle, ellipse etc. in images is one of the most significant topics in diverse areas such as image and signal processing, pattern recognition and remote sensing. Compressive Sensing(CS) theory details how the signal is sparsely reconstructed in a known basis from low number of linear measurement. Sparsity of parametric shapes in parameter space offers to detect parametric shapes from low number of linear measurements under frameworks proposed by CS methods. Joint detection performance of different parametric shapes in image is studied under different small number of measurements and noise level. Because of being both discrete image space and discretized parameter space, effect of offgrid, one of the most important problem in CS, is analysed in terms of shape detection. Results show that parametric shapes can robustly be found with a few measurements and effects of offgrid are seen as distribution of target energy in parameter space.