The technique of obtaining information or data about any feature or object from afar, called in technical parlance as remote sensing, has proven extremely useful in diverse fields. In the ecological sphere, especially, remote sensing has enabled collection of data or information about large swaths of areas or landscapes. Even then, in remote sensing the task of identifying and monitoring of different water reservoirs has proved a tough one. This is mainly because getting correct appraisals about the spread and boundaries of the area under study and the contours of any water surfaces lodged therein becomes a factor of utmost importance. Identification of water reservoirs is rendered even tougher because of presence of cloud in satellite images, which becomes the largest source of error in identification of water surfaces. To overcome this glitch, the method of the shape matching approach for analysis of cloudy images in reference to cloud-free images of water surfaces with the help of vector data processing, is recommended. It includes the database of water bodies in vector format, which is a complex polygon structure. This analysis highlights three steps: First, the creation of vector database for the analysis; second, simplification of multi-scale vector polygon features; and third, the matching of reference and target water bodies database within defined distance tolerance. This feature matching approach provides matching of one to many and many to many features. It also gives the corrected images that are free of clouds.

Proper identification of oriented knots and 2-component links requires a precise link nomenclature. Motivated by questions arising in DNA topology, this study aims to produce a nomenclature unambiguous with respect to link symmetries. For knots, this involves distinguishing a knot type from its mirror image. In the case of 2-component links, there are up to sixteen possible symmetry types for each topology. The study revisits the methods previously used to disambiguate chiral knots and extends them to oriented 2-component links with up to nine crossings. Monte Carlo simulations are used to report on writhe, a geometric indicator of chirality. There are ninety-two prime 2-component links with up to nine crossings. Guided by geometrical data, linking number and the symmetry groups of 2-component links, a canonical link diagram for each link type is proposed. All diagrams but six were unambiguously chosen ( $8_1^{2}5$ , $9_5^2$ , $9_3^{2}4$ , $9_3^{2}5$ , $9_3^{2}9$ , and $9_4^{2}1$ ). We include complete tables for prime knots with up to ten crossings and prime links with up to nine crossings. We also prove a result on the behavior of the writhe under local lattice moves.

Every biological image contains quantitative data that can be used to test hypotheses about how patterns were formed, what entities are associated with one another, and whether standard mathematical methods inform our understanding of biological phenomena. In particular, spatial point distributions and polygonal tessellations are particularly amendable to analysis with a variety of graph theoretic, computational geometric, and spatial statistical tools such as: Voronoi Polygons; Delaunay Triangulations; Perpendicular Bisectors; Circumcenters; Convex Hulls; Minimal Spanning Trees; Ulam Trees; Pitteway Violations; Circularity; Clark-Evans spatial statistics; Variance to Mean Ratios; Gabriel Graphs; and, Minimal Spanning Trees. Furthermore, biologists have developed a number of empirically related correlations for polygonal tessellations such as: Lewis’s Law (the number of edges of convex polygons are positively correlated with the areas of these polygons): Desch’s Law (the number of edges of convex polygons are positively correlated with the perimeters of these polygons); and Errara’s Law (daughter cell areas should be roughly half that of their parent cells’ areas). We introduce a new Pitteway Law that the number of sides of the convex polygons in a Voronoi tessellation of biological epithelia is proportional to the minimal interior angle of the convex polygons as angles less than 90 degrees result in Pitteway violations of the Delaunay dual of the Voronoi tessellation.