The shape of objects seen in images depends on the viewpoint. This effect confounds recognition. We demonstrate a theoretical framework within which it is possible to construct descriptors for both curves and surfaces, which do not vary with viewpoint. These descriptors are known as invariants. We use this framework to construct invariant shape descriptors for plane curves. These invariant shap...

Motivated by the problem of analyzing shapes of fiber tracts in DT-MRI data, we present a geometric framework for studying shapes of open curves in R. We start with a space of unit-length curves and define the shape space to be its quotient space modulo rotation and reparametrization groups. Thus, the resulting shape analysis is invariant to parameterizations of curves. Furthermore, a Riemannia...

This paper illustrates and extends an efficient framework, called the square-root-elastic (SRE) framework, for studying shapes of closed curves, that was first introduced in [2]. This framework combines the strengths of two important ideas - elastic shape metric and path-straightening methods - for finding geodesics in shape spaces of curves. The elastic metric allows for optimal matching of fe...

in the present paper, the deformation zone of the ecae (equal channel angular extrusion) process was investigated using the upper bound theorem. for this purpose, the shape of the streamlines in the deformation zone was assumed to be cubic bezier curves. then, the force required for the ecae process was optimized with regard to the parameters defining the shape of streamlines by the upper bound...

measurement of chlorophyll fluorescence is noninvasive, highly sensitive, fast and easy way to give important information about the photosynthetic apparatus. chlorophyll fluorescence parameters and kautsky curves of wild oat and wild mustard sprayed by clodinafop and dicamba+2, 4-d respectively was investigated at two green house experiments. the results indicated significant reduction at trend...

In this work, we find meaningful parameterizations of cortical surfaces utilizing prior anatomical information in the form of anatomical landmarks (sulci curves) on the surfaces. Specifically we generate close to conformal parametrizations that also give a shape-based correspondence between the landmark curves. We propose a variational energy that measures the harmonic energy of the parameteriz...

We present a quantitative approach to the measurement of shape dissimilarity between two 3D (three-dimensional) curves. Any 3D continuous curve can be digitalized and represented as a 3D discrete curve. Thus, a 3D discrete curve is composed of constant orthogonal straightline segments. In order to represent 3D discrete curves, we use the orthogonal direction change chain code. The chain element...

this paper presents a description of the equipment, testing procedure, and methodology to obtain ground mechanical parameters. the p-y curves for laterally loaded piles are developed. methods for the development of p-y curves from pressure meter and dilatometer (dmt) test are described. p-y curves are used in the analysis to represent lateral soil-pile interaction. the pressure meter offers an ...