We consider the problem of learning an object model for feature matching. The matching system is Bayesian in nature with separate likelihood and prior parts. The likelihood is based on Gabor filter responses, which are modelled as probability distributions in the filter response vector space. The prior model for the object shape is learnt in two stages: in the first stage we assume only the mea...

The variance of fuzzy random variables often appears in fuzzy random programming problems. Based on the definition of the variance of a fuzzy random variable, this paper attempts to deduce several formulas for the variances of trapezoidal fuzzy random variables, in which the randomness is characterized by uniform distribution. Firstly, we give the moment formulas for trapezoidal fuzzy variables...

In this paper, we present a new prioritization method for information fusion under fuzzy environment. We propose a new measure to measure the similarity between generalized trapezoidal fuzzy numbers. Based on the proposed similarity measure, we develop an utility function of generalized trapezoidal fuzzy numbers. With the utility function of generalized trapezoidal fuzzy numbers, we propose a n...

This paper proposes the concepts of a neutrosophic number and a trapezoidal neutrosophic number (TNN), the basic operational relations of TNNs, and the score function of TNN. Then, we develop a trapezoidal neutrosophic weighted arithmetic averaging (TNWAA) operator and a trapezoidal neutrosophic weighted geometric averaging (TNWGA) operator to aggregate TNN information and investigate their pro...

The features of a class of cubic curves with a shape factor are analyzed by means of the theory of envelope and topological mapping. The effects of the shape factor on the cubic curves are made clear. Necessary and sufficient conditions are derived for the curve to have one or two inflection points, a loop or a cusp, or to be locally or globally convex. Those conditions are completely character...

The paper discusses how the set of shape primitives to be used for decomposing a shape into meaningful parts may affect the performance of the decomposition method, and proposes a new set of shape primitives to be used when the input shape is represented by its skeleton. The suggested shape primitives comhine the qualitative, general notion of shape needed to cope with the large variability of ...

The features of a class of cubic curves with a shape factor are analyzed by means of the theory of envelope and topological mapping. The effects of the shape factor on the cubic curves are made clear. Necessary and sufficient conditions are derived for the curve to have one or two inflection points, a loop or a cusp, or to be locally or globally convex. Those conditions are completely character...

One of the challenging problems for shape editing is to adapt shapes with diversified structures for various editing needs. In this paper we introduce a shape editing approach that automatically adapts the structure of a shape being edited with respect to user inputs. Given a category of shapes, our approach first classifies them into groups based on the constituent parts. The group-sensitive p...

We propose a general method for finding pointwise correspondence between 2-D shapes based on the concept of order structure and using geometric hashing. The problem of finding correspondence and the problem of establishing shape equivalence can be considered as one and the same problem. Given shape equivalence, we can in general find pointwise correspondence and the existence of a unambiguous c...

We show that the E +-class can be decided by a liftable order, when it is applied a posteriori. This is a surprising result, because the E +-class was one of the motivations for the study of non-liftable orders. Also surprising is the behaviour of the resolution process. Initially the variable depth of the clauses may grow, but it will not grow deeper than a certain bound. We do not make use of...