This article discusses the question of how noise affects the discrimination of the boundaries (contours) between the regions of a tomographic image and, as a consequence, the segmentation of the image. The discrimination of boundaries is associated with differentiation of the image, while the differentiation of noisy functions is an ill-posed problem (unstable with respect to noise on the image). It is proposed to suppress noise not only by well-known filtering methods but also by means of smoothing (approximating) splines. The numerical examples given here show that the boundaries are discriminated more accurately as a result of using splines.
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