793,767 research outputs found
Multi-set canonical correlation analysis for 3D abnormal gait behaviour recognition based on virtual sample generation
Small sample dataset and two-dimensional (2D) approach are challenges to vision-based abnormal gait behaviour recognition (AGBR). The lack of three-dimensional (3D) structure of the human body causes 2D based methods to be limited in abnormal gait virtual sample generation (VSG). In this paper, 3D AGBR based on VSG and multi-set canonical correlation analysis (3D-AGRBMCCA) is proposed. First, the unstructured point cloud data of gait are obtained by using a structured light sensor. A 3D parametric body model is then deformed to fit the point cloud data, both in shape and posture. The features of point cloud data are then converted to a high-level structured representation of the body. The parametric body model is used for VSG based on the estimated body pose and shape data. Symmetry virtual samples, pose-perturbation virtual samples and various body-shape virtual samples with multi-views are generated to extend the training samples. The spatial-temporal features of the abnormal gait behaviour from different views, body pose and shape parameters are then extracted by convolutional neural network based Long Short-Term Memory model network. These are projected onto a uniform pattern space using deep learning based multi-set canonical correlation analysis. Experiments on four publicly available datasets show the proposed system performs well under various conditions
Autocalibration with the Minimum Number of Cameras with Known Pixel Shape
In 3D reconstruction, the recovery of the calibration parameters of the
cameras is paramount since it provides metric information about the observed
scene, e.g., measures of angles and ratios of distances. Autocalibration
enables the estimation of the camera parameters without using a calibration
device, but by enforcing simple constraints on the camera parameters. In the
absence of information about the internal camera parameters such as the focal
length and the principal point, the knowledge of the camera pixel shape is
usually the only available constraint. Given a projective reconstruction of a
rigid scene, we address the problem of the autocalibration of a minimal set of
cameras with known pixel shape and otherwise arbitrarily varying intrinsic and
extrinsic parameters. We propose an algorithm that only requires 5 cameras (the
theoretical minimum), thus halving the number of cameras required by previous
algorithms based on the same constraint. To this purpose, we introduce as our
basic geometric tool the six-line conic variety (SLCV), consisting in the set
of planes intersecting six given lines of 3D space in points of a conic. We
show that the set of solutions of the Euclidean upgrading problem for three
cameras with known pixel shape can be parameterized in a computationally
efficient way. This parameterization is then used to solve autocalibration from
five or more cameras, reducing the three-dimensional search space to a
two-dimensional one. We provide experiments with real images showing the good
performance of the technique.Comment: 19 pages, 14 figures, 7 tables, J. Math. Imaging Vi
On the non-local geometry of turbulence
A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed
3D printing dimensional calibration shape: Clebsch Cubic
3D printing and other layer manufacturing processes are challenged by
dimensional accuracy. Several techniques are used to validate and calibrate
dimensional accuracy through the complete building envelope. The validation
process involves the growing and measuring of a shape with known parameters.
The measured result is compared with the intended digital model. Processes with
the risk of deformation after time or post processing may find this technique
beneficial. We propose to use objects from algebraic geometry as test shapes. A
cubic surface is given as the zero set of a 3rd degree polynomial with 3
variables. A class of cubics in real 3D space contains exactly 27 real lines.
We provide a library for the computer algebra system Singular which, from 6
given points in the plane, constructs a cubic and the lines on it. A surface
shape derived from a cubic offers simplicity to the dimensional comparison
process, in that the straight lines and many other features can be analytically
determined and easily measured using non-digital equipment. For example, the
surface contains so-called Eckardt points, in each of which three of the lines
intersect, and also other intersection points of pairs of lines. Distances
between these intersection points can easily be measured, since the points are
connected by straight lines. At all intersection points of lines, angles can be
verified. Hence, many features distributed over the build volume are known
analytically, and can be used for the validation process. Due to the thin shape
geometry the material required to produce an algebraic surface is minimal. This
paper is the first in a series that proposes the process chain to first define
a cubic with a configuration of lines in a given print volume and then to
develop the point cloud for the final manufacturing. Simple measuring
techniques are recommended.Comment: 8 pages, 1 figure, 1 tabl
Estimating average growth trajectories in shape-space using kernel smoothing
In this paper, we show how a dense surface point distribution model of the human face can be computed and demonstrate the usefulness of the high-dimensional shape-space for expressing the shape changes associated with growth and aging. We show how average growth trajectories for the human face can be computed in the absence of longitudinal data by using kernel smoothing across a population. A training set of three-dimensional surface scans of 199 male and 201 female subjects of between 0 and 50 years of age is used to build the model
Reconciling landmarks and level sets: geometric shape warping and matching using generalized gradients and correspondence-augmented implicit representations
Shape warping is a key problem in statistical shape analysis. This paper proposes a framework for geometric shape warping based on both shape distances and landmarks. Taking advantage of the recently proposed spatially coherent flows, our method is mathematically well-posed and uses only intrinsic shape information, namely some similarity measure between shapes and the correspondence of landmarks provided on the shape surface. No extrinsic quantity is considered, neither a diffeomorphism of the embedding space nor point correspondences in this space. Thanks to a recent extension of the level set method allowing point tracking and tangential velocities, our method is compatible with implicit representations. Moreover, a matching between shape surfaces is provided at no additional cost. Although some recent work deals with implicit representations and landmarks, it is, to our knowledge, the first time that landmarks and shape distances are reconciled in a pure geometric level set framework. The feasibility of the method is demonstrated with two- and three-dimensional examples. Combining shape distance and landmarks, our approach reveals to need only a small number of landmarks to obtain improvements on both warping and matching
- …