Some results on p-shape curvatures of non-lightlike space curves

In this paper, we obtain some findings for a non-null curve parameterized by spherical arc length. We investigate the relationship between a non-null curve with p-shape curvatures and pseudospherical curves on S21 and H2(−1). We introduce the concept of similar helix in Minkowski 3-space E31. Besides, we explicitly determine the parametrizations of all non-lightlike self-similar curves by using the pseudo-spherical curves in E31.No sponso

Similar and self-similar curves in minkowski n-space

In this paper, we investigate the similarity transformations in the Minkowski n-space. We study the geometric invariants of nonnull curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null curve according to a similarity motion of En1. We determine the parametrizations of non-null self-similar curves in En1. .No sponso

Objective estimation of body condition score by modeling cow body shape from digital images.

Body condition score (BCS) is considered an important tool for management of dairy cattle. The feasibility of estimating the BCS from digital images has been demonstrated in recent work. Regression machines have been successfully employed for automatic BCS estimation, taking into account information of the overall shape or information extracted on anatomical points of the shape. Despite the progress in this research area, such studies have not addressed the problem of modeling the shape of cows to build a robust descriptor for automatic BCS estimation. Moreover, a benchmark data set of images meant as a point of reference for quantitative evaluation and comparison of different automatic estimation methods for BCS is lacking. The main objective of this study was to develop a technique that was able to describe the body shape of cows in a reconstructive way. Images, used to build a benchmark data set for developing an automatic system for BCS, were taken using a camera placed above an exit gate from the milking robot. The camera was positioned at 3 m from the ground and in such a position to capture images of the rear, dorsal pelvic, and loin area of cows. The BCS of each cow was estimated on site by 2 technicians and associated to the cow images. The benchmark data set contained 286 images with associated BCS, anatomical points, and shapes. It was used for quantitative evaluation. A set of example cow body shapes was created. Linear and polynomial kernel principal component analysis was used to reconstruct shapes of cows using a linear combination of basic shapes constructed from the example database. In this manner, a cow's body shape was described by considering her variability from the average shape. The method produced a compact description of the shape to be used for automatic estimation of BCS. Model validation showed that the polynomial model proposed in this study performs better (error=0.31) than other state-of-the-art methods in estimating BCS even at the extreme values of BCS scale