Directional Geodesic Active Contours

We present a non-conformal metric that generalizes the geodesic active contours approach for image segmentation. The new metric is obtained by adding to the Euclidean metric an additional term that penalizes the misalignment of the curve with the image gradient and multiplying the resulting metric by a conformal factor that depends on the edge intensity. In this way, a closer fitting to the edge direction results. The provided experimental results address the computation of the geodesics of the new metric by applying a gradient descent to externally provided curves. The good performance of the proposed techniques is demonstrated in comparison with other active contours methods

APPLICATIONS OF THE MEAN CURVATURE FLOW ASSOCIATED TO ANISOTROPIC GENERALIZED LAGRANGE METRICS IN IMAGE PROCESSING

The Geodesic Active Field (GAF) approach from image processing - whose mathematical background is the Riemannian theory of submanifolds, was recently extended by the authors to the Finslerian setting, for certain specific metrics of Randers type.      The present work studies the significantly more flexible Generalized Lagrange (GL) extension,      which allows a versatile adapting of the GAF process to Finslerian, pseudo-Finslerian and      Lagrangian structures.      The mathematically essential GAF mean curvature flow PDEs of three such GL structures      (Randers-Ingarden, Synge-Beil and proper Generalized Lagrange) are explicitly obtained,      discussed, implemented, and their corresponding feature evolution is compared with the      classic results produced by the established original Riemannian GAF model

Anizotropna radna okruženja za dinamičke sisteme i obradu slika

The research topic of this PhD thesis is a comparative analysis of classical specic geometric frameworks and of their anisotropic extensions; the construction of three different types of Finsler frameworks, which are suitable for the analysis of the cancer cells population dynamical system; the development of the anisotropic Beltrami framework theory with the derivation of the evolution ow equations corresponding to different classes of anisotropic metrics, and tentative applications in image processing.Predmet istraživanja doktorske disertacije je uporedna analiza klasičnih i specifičnih geometrijskih radnih okruženja i njihovih anizotropnih proširenja; konstrukcija  tri Finslerova radna okruženja različitog tipa koja su pogodna za analizu dinamičkog  sistema populacije kanceroznih ćelija; razvoj teorije anizotropnog Beltramijevog radnog okruženja i formiranje jednačina evolutivnog toka za različite klase anizotropnih metrika, kao i mogućnost primene dobijenih teorijskih rezultata u digitalnoj obradi slika