Character (mathematics)

About: Character (mathematics) is a research topic. Over the lifetime, 46723 publications have been published within this topic receiving 411412 citations.

A survey of methods and strategies in character segmentation

Abstract: Character segmentation has long been a critical area of the OCR process. The higher recognition rates for isolated characters vs. those obtained for words and connected character strings well illustrate this fact. A good part of recent progress in reading unconstrained printed and written text may be ascribed to more insightful handling of segmentation. This paper provides a review of these advances. The aim is to provide an appreciation for the range of techniques that have been developed, rather than to simply list sources. Segmentation methods are listed under four main headings. What may be termed the "classical" approach consists of methods that partition the input image into subimages, which are then classified. The operation of attempting to decompose the image into classifiable units is called "dissection." The second class of methods avoids dissection, and segments the image either explicitly, by classification of prespecified windows, or implicitly by classification of subsets of spatial features collected from the image as a whole. The third strategy is a hybrid of the first two, employing dissection together with recombination rules to define potential segments, but using classification to select from the range of admissible segmentation possibilities offered by these subimages. Finally, holistic approaches that avoid segmentation by recognizing entire character strings as units are described.

Spacetime constraints

Abstract: Spacetime constraints are a new method for creating character animation. The animator specifies what the character has to do, for instance, "jump from here to there, clearing a hurdle in between;" how the motion should be performed, for instance "don't waste energy," or "come down hard enough to splatter whatever you land on;" the character's physical structure---the geometry, mass, connectivity, etc. of the parts; and the physical resources' available to the character to accomplish the motion, for instance the character's muscles, a floor to push off from, etc. The requirements contained in this description, together with Newton's laws, comprise a problem of constrained optimization. The solution to this problem is a physically valid motion satisfying the "what" constraints and optimizing the "how" criteria. We present as examples a Luxo lamp performing a variety of coordinated motions. These realistic motions conform to such principles of traditional animation as anticipation, squash-and-stretch, follow-through, and timing.

Stochastic mapping of morphological characters.

Abstract: Many questions in evolutionary biology are best addressed by comparing traits in different species Often such studies involve mapping characters on phylogenetic trees Mapping characters on trees allows the nature, number, and timing of the transformations to be identified The parsimony method is the only method available for mapping morphological characters on phylogenies Although the parsimony method often makes reasonable reconstructions of the history of a character, it has a number of limitations These limitations include the inability to consider more than a single change along a branch on a tree and the uncoupling of evolutionary time from amount of character change We extended a method described by Nielsen (2002, Syst Biol 51:729-739) to the mapping of morphological characters under continuous-time Markov models and demonstrate here the utility of the method for mapping characters on trees and for identifying character correlation (Bayesian estimation; character correlation; character mapping; Markov chain Monte Carlo) The footprint of natural selection on organisms can of- ten be detected using phylogenetic methods Correlation in either molecular or morphological characters is taken as evidence of natural selection acting on those charac- ters (Harvey and Pagel, 1991) The correlation might be between a character and the environment, with the re- peated evolution of the character in a particular environ- ment indicating that the trait confers an advantage, or the correlation may be between one character and another In ribosomal RNA sequences, for example, correlated changes occur in nucleotides paired in the stem struc- tures; natural selection is acting to maintain Watson- Crick pairing of nucleotides in the functionally impor- tant stem structures In either case-correlation between different characters or the repeated evolution of a charac- ter in a particular environment-phylogenetic methods provide the best framework for the analysis of correlation because they allow the effects of a common phylogenetic history that simultaneously acts on all of the characters to be partitioned from the evolutionary processes gener- ating the character patterns (Felsenstein, 1985) Despite the importance of phylogenetic analysis of character change in evolutionary biology, detection of correlation in characters is fraught with difficulties One dilemma involves how characters should be mapped onto a phylogenetic tree Many methods for detecting correlations rely on mapping character changes on a phylogenetic tree using the parsimony method (Ridley, 1983; Maddison, 1990) The parsimony method provides the minimum number of transformations required to explain the evolution of the character on the tree and therefore necessarily underestimates the total number of changes Furthermore, some methods treat the par- simony mapping of a character as an observation in fur- ther statistical analyses (Ridley, 1983; Maddison, 1990) Although the parsimony method is expected to provide a reasonable mapping of a character when the rates of evolution are low, the fundamental problem with the method is that it does not account for the uncertainty in the process of character change In effect, the parsimony method wagers all on the mapping requiring the fewest changes, when in reality many other perhaps slightly less parsimonious mappings may be nearly as good or