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An approach to construction of robust features is proposed and applied to an instance of the correspondence problem. The main idea is to construct a synthetic image by a multiresolution sketch (MS) of an image and involve it into extraction of the invariants. The MS is constructed by processing the image with a scalable detector of the semilocal 1D-elements. Then, a synthetic image is constructed with all elements of the MS. Local maxima of the first and second derivatives of the synthetic image along discrete curves of the MS lead to some singular elements represented by the points of a 4D manifold. It turns out that a representative subset of the singular elements is stable. To prove that, the pair-wise correspondence between subsets of singular elements of two shots of a film was established experimentally by a consistency technique, which, unlike past approaches, does not involve epipolar constraints.