This article investigates the restoration of ultrasonic pulse-echo C-scan images by means of deconvolution with a point spread function (PSF). The deconvolution concept from linear system theory (LST) is linked to the wave equation formulation of the imaging process, and an analytic formula for the PSF of planar transducers is derived. For this analytic expression, different numerical and analytic approximation schemes for evaluating the PSF are presented. By comparing simulated images with measured C-scan images, we demonstrate that the assumptions of LST in combination with our formula for the PSF are a good model for the pulse-echo imaging process. To reconstruct the object from a C-scan image, we compare different deconvolution schemes: the Wiener filter, the ForWaRD algorithm, and the Richardson-Lucy algorithm. The best results are obtained with the Richardson-Lucy algorithm with total variation regularization. For distances greater or equal twice the near field distance, our experiments show that the numerically computed PSF can be replaced with a simple closed analytic term based on a far field approximation.

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Abstract:This article proposes a new method for detecting symmetry points in images. Like other symmetry detection algorithms, it assigns a "symmetry score" to each image point. Our symmetry measure is only based on scalar products between gradients and is therefore both easy to implement and of low runtime complexity. Moreover, our approach also yields the size of the symmetry region without additional computational effort. As both axial symmetries as well as some rotational symmetries can result in a point symmetry, we propose and evaluate different methods for identifying the rotational symmetries. We evaluate our method on two different test sets of real world images and compare it to several other rotational symmetry detection methods.

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