Matches in SemOpenAlex for { <https://semopenalex.org/work/W2897345496> ?p ?o ?g. }
Showing items 1 to 91 of
91
with 100 items per page.
- W2897345496 abstract "A set in the Euclidean plane is said to be $theta$-biconvex, for some $thetain[0,pi/2)$, when all its sections along the directions $theta$ and $theta+pi/2$ are convex sets in the real line. Biconvexity is a natural notion with some useful applications in optimization theory. It has also be independently used, under the name of `rectilinear convexity', in computational geometry. We are concerned here with the problem of asymptotically reconstructing (or estimating) a biconvex set $S$ from a random sample of points drawn on $S$. By analogy with the classical convex case, one would like to define the `biconvex hull' of the sample points as a natural estimator for $S$. However, as previously pointed out by several authors, the notion of `hull' for a given set $A$ (understood as the `minimal' set including $A$ and having the required property) has no obvious, useful translation to the biconvex case. This is in sharp contrast with the well-known elementary definition of convex hull. Thus, we have selected the most commonly accepted notion of `biconvex hull' (often called `rectilinear convex hull'): we first provide additional motivations for this definition, proving some useful relations with other convexity-related notions. Then, we prove some results concerning the consistent approximation (with respect to the Hausdorff metric) of a biconvex set $S$ and and the corresponding biconvex hull. An analogous result is also provided for the boundaries. A method to approximate (from a sample of points on $S$) the biconvexity angle $theta$ is also given." @default.
- W2897345496 created "2018-10-26" @default.
- W2897345496 creator A5070470540 @default.
- W2897345496 creator A5091141642 @default.
- W2897345496 date "2018-10-18" @default.
- W2897345496 modified "2023-09-27" @default.
- W2897345496 title "On estimation of biconvex sets" @default.
- W2897345496 hasPublicationYear "2018" @default.
- W2897345496 type Work @default.
- W2897345496 sameAs 2897345496 @default.
- W2897345496 citedByCount "0" @default.
- W2897345496 crossrefType "posted-content" @default.
- W2897345496 hasAuthorship W2897345496A5070470540 @default.
- W2897345496 hasAuthorship W2897345496A5091141642 @default.
- W2897345496 hasConcept C105795698 @default.
- W2897345496 hasConcept C106159729 @default.
- W2897345496 hasConcept C112680207 @default.
- W2897345496 hasConcept C114614502 @default.
- W2897345496 hasConcept C127413603 @default.
- W2897345496 hasConcept C129782007 @default.
- W2897345496 hasConcept C134306372 @default.
- W2897345496 hasConcept C157972887 @default.
- W2897345496 hasConcept C162324750 @default.
- W2897345496 hasConcept C177264268 @default.
- W2897345496 hasConcept C17825722 @default.
- W2897345496 hasConcept C185429906 @default.
- W2897345496 hasConcept C185592680 @default.
- W2897345496 hasConcept C198531522 @default.
- W2897345496 hasConcept C199104240 @default.
- W2897345496 hasConcept C199360897 @default.
- W2897345496 hasConcept C206194317 @default.
- W2897345496 hasConcept C2524010 @default.
- W2897345496 hasConcept C28826006 @default.
- W2897345496 hasConcept C33923547 @default.
- W2897345496 hasConcept C37423430 @default.
- W2897345496 hasConcept C41008148 @default.
- W2897345496 hasConcept C43617362 @default.
- W2897345496 hasConcept C49870271 @default.
- W2897345496 hasConcept C72134830 @default.
- W2897345496 hasConceptScore W2897345496C105795698 @default.
- W2897345496 hasConceptScore W2897345496C106159729 @default.
- W2897345496 hasConceptScore W2897345496C112680207 @default.
- W2897345496 hasConceptScore W2897345496C114614502 @default.
- W2897345496 hasConceptScore W2897345496C127413603 @default.
- W2897345496 hasConceptScore W2897345496C129782007 @default.
- W2897345496 hasConceptScore W2897345496C134306372 @default.
- W2897345496 hasConceptScore W2897345496C157972887 @default.
- W2897345496 hasConceptScore W2897345496C162324750 @default.
- W2897345496 hasConceptScore W2897345496C177264268 @default.
- W2897345496 hasConceptScore W2897345496C17825722 @default.
- W2897345496 hasConceptScore W2897345496C185429906 @default.
- W2897345496 hasConceptScore W2897345496C185592680 @default.
- W2897345496 hasConceptScore W2897345496C198531522 @default.
- W2897345496 hasConceptScore W2897345496C199104240 @default.
- W2897345496 hasConceptScore W2897345496C199360897 @default.
- W2897345496 hasConceptScore W2897345496C206194317 @default.
- W2897345496 hasConceptScore W2897345496C2524010 @default.
- W2897345496 hasConceptScore W2897345496C28826006 @default.
- W2897345496 hasConceptScore W2897345496C33923547 @default.
- W2897345496 hasConceptScore W2897345496C37423430 @default.
- W2897345496 hasConceptScore W2897345496C41008148 @default.
- W2897345496 hasConceptScore W2897345496C43617362 @default.
- W2897345496 hasConceptScore W2897345496C49870271 @default.
- W2897345496 hasConceptScore W2897345496C72134830 @default.
- W2897345496 hasLocation W28973454961 @default.
- W2897345496 hasOpenAccess W2897345496 @default.
- W2897345496 hasPrimaryLocation W28973454961 @default.
- W2897345496 hasRelatedWork W137282128 @default.
- W2897345496 hasRelatedWork W145110004 @default.
- W2897345496 hasRelatedWork W1510770274 @default.
- W2897345496 hasRelatedWork W1702184388 @default.
- W2897345496 hasRelatedWork W1823264389 @default.
- W2897345496 hasRelatedWork W2007030377 @default.
- W2897345496 hasRelatedWork W2117218580 @default.
- W2897345496 hasRelatedWork W2351363760 @default.
- W2897345496 hasRelatedWork W2377563771 @default.
- W2897345496 hasRelatedWork W2591596833 @default.
- W2897345496 hasRelatedWork W2778738010 @default.
- W2897345496 hasRelatedWork W2885392891 @default.
- W2897345496 hasRelatedWork W2952448168 @default.
- W2897345496 hasRelatedWork W2963937081 @default.
- W2897345496 hasRelatedWork W2972122392 @default.
- W2897345496 hasRelatedWork W2978113281 @default.
- W2897345496 hasRelatedWork W3022908936 @default.
- W2897345496 hasRelatedWork W3036951877 @default.
- W2897345496 hasRelatedWork W3124631557 @default.
- W2897345496 hasRelatedWork W39773989 @default.
- W2897345496 isParatext "false" @default.
- W2897345496 isRetracted "false" @default.
- W2897345496 magId "2897345496" @default.
- W2897345496 workType "article" @default.