\nWe study different relaxations of non-convex functionals that can be found in image processing. Some problems, such as image segmentation, can indeed be written as the minimization of a functional. The minimizer of the functional represents the segmentation. <\/p>\n
Different methods have been proposed in order to find local or global minima of the non-convex functional of the two-phase piecewise constant Mumford-Shah model. With a convex relaxation of this model we can find a global minimum of the non-convex functional. We present and compare some of these methods and we propose a new model with a narrow band. This models finds local minima while using robust convex optimization algorithms. Then a convex relaxation of a two-phase segmentation model is built that compares two given histograms with those of the two segmented regions.<\/p>\n
We also study some relaxations of high-dimension multi-label problems such as optical flow computation. A convex relaxation with a new algorithm is proposed. The algorithm is iterative with exact projections. A new algorithm is given for a relaxation that is convex in each variable but that is not convex globally. We study the problem of constructing a solution of the original non-convex problem with a solution of the relaxed problem. We compare existing methods with new ones.<\/p>\n
<\/p>","protected":false},"excerpt":{"rendered":"
We study different relaxations of non-convex functionals that can be found in image processing. Some problems, such as image segmentation, can indeed be written as the minimization of a functional. The minimizer of the functional represents the segmentation. Different methods have been proposed in order to find local or global minima of the non-convex functional […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25,24,16],"tags":[],"class_list":["post-694","post","type-post","status-publish","format-standard","hentry","category-segmentation","category-optimization","category-traitement-dimages"],"_links":{"self":[{"href":"https:\/\/image.math.u-bordeaux.fr\/index.php?rest_route=\/wp\/v2\/posts\/694","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/image.math.u-bordeaux.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/image.math.u-bordeaux.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/image.math.u-bordeaux.fr\/index.php?rest_route=\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/image.math.u-bordeaux.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=694"}],"version-history":[{"count":5,"href":"https:\/\/image.math.u-bordeaux.fr\/index.php?rest_route=\/wp\/v2\/posts\/694\/revisions"}],"predecessor-version":[{"id":765,"href":"https:\/\/image.math.u-bordeaux.fr\/index.php?rest_route=\/wp\/v2\/posts\/694\/revisions\/765"}],"wp:attachment":[{"href":"https:\/\/image.math.u-bordeaux.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=694"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/image.math.u-bordeaux.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=694"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/image.math.u-bordeaux.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=694"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}