A Robust Method for Estimating Image Geometry With Local Structure Constraint
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Abstract:
The estimation of image geometry benefits many applications in the field of computer vision, such as stereo correspondence, 3-D reconstruction, and camera self-calibration. It is very challenging since the proportion of inliers in putative correspondences is usually very low, and traditional image geometry estimation methods (such as Ransac) suffer from low accuracy at a high outlier ratio. In this paper, we tackle the two-view image geometry estimation problem and propose a new robust estimation method L 2 E-LSC (short for L 2 E with local structure constraint) based on the L 2 E algorithm. In particular, we first establish initial correspondences by feature description matches, and then estimate the fundamental matrix and homography using L 2 E-LSC and get the refined correspondences. The L 2 E-LSC is able to robustly deal with the noise and outliers contained in point correspondences. Extensive experiments conducted on real images from public available datasets have demonstrated that it can achieve good estimation accuracy and superior performance over previous approaches, particularly when there are severe outliers.Keywords:
Computational Geometry
Sequence (biology)
Positive selection
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The iPatch computer code for intelligently patching surface grids was developed to convert conceptual geometry to computational fluid dynamics (CFD) geometry (see figure). It automatically uses bicubic B-splines to extrapolate (if necessary) each surface in a conceptual geometry so that all the independently defined geometric components (such as wing and fuselage) can be intersected to form a watertight CFD geometry. The software also computes the intersection curves of surface patches at any resolution (up to 10.4 accuracy) specified by the user, and it writes the B-spline surface patches, and the corresponding boundary points, for the watertight CFD geometry in the format that can be directly used by the grid generation tool VGRID. iPatch requires that input geometry be in PLOT3D format where each component surface is defined by a rectangular grid {(x(i,j), y(i,j), z(i,j)):1less than or equal to i less than or equal to m, 1 less than or equal to j less than or equal to n} that represents a smooth B-spline surface. All surfaces in the PLOT3D file conceptually represent a watertight geometry of components of an aircraft on the half-space y greater than or equal to 0. Overlapping surfaces are not allowed, but could be fixed by a utility code fixp3d. The fixp3d utility code first finds the two grid lines on the two surface grids that are closest to each other in Hausdorff distance (a metric to measure the discrepancies of two sets); then uses one of the grid lines as the transition line, extending grid lines on one grid to the other grid to form a merged grid. Any two connecting surfaces shall have a visually common boundary curve, or can be described by an intersection relationship defined in a geometry specification file. The intersection of two surfaces can be at a conceptual level. However, the intersection is directional (along either i or j index direction), and each intersecting grid line (or its spine extrapolation) on the first surface should intersect the second surface. No two intersection relationships will result in a common intersection point of three surfaces. The output files of iPatch are IGES, d3m, and mapbc files that define the CFD geometry in VGRID format. The IGES file gives the NURBS definition of the outer mold line in the geometry. The d3m file defines how the outer mold line is broken into surface patches whose boundary curves are defined by points. The mapbc file specifies what the boundary condition is on each patch and the corresponding NURBS surface definition of each non-planar patch in the IGES file.
Computational Geometry
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In our study of 2D connections between objects, we used some simple constraint devices, such as the contact point and the link with pivoting end connections. We learned that these constraint devices are functionally equivalent for small motions and that for the purpose of our analysis, it does not matter which constraint device we decide to use. It is only important to know whether and where constraints are applied.
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Computational Information Geometry... ...in mixture modelling Computational Information Geometry: mixture modelling Germain Van Bever1 , R. Sabolova1 , F. Critchley1 & P. Marriott2 . 1 The Open University (EPSRC grant EP/L010429/1), United Kingdom 2 University of Waterloo, USA GSI15, 28-30 October 2015, Paris Germain Van Bever CIG for mixtures 1/19 Computational Information Geometry... ...in mixture modelling Outline 1 Computational Information Geometry... Information Geometry CIG 2 ...in mixture modelling Introduction Lindsay’s convex geometry (C)IG for mixture distributions Germain Van Bever CIG for mixtures 2/19 Computational Information Geometry... ...in mixture modelling Information Geometry CIG Outline 1 Computational Information Geometry... Information Geometry CIG 2 ...in mixture modelling Introduction Lindsay’s convex geometry (C)IG for mixture distributions Germain Van Bever CIG for mixtures 3/19 Computational Information Geometry... ...in mixture modelling Information Geometry CIG Generalities The use of geometry in statistics gave birth to many different approaches. Traditionally, Information geometry refers to the application of differential geometry to statistica
Computational Geometry
Convex geometry
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In this paper we present a method for geometry synthesis by example, inspired by techniques from texture synthesis. Given an example of input geometry, we synthesize new output geometry that is perceived similar to the input geometry, but at the same time differs in its local appearance. We assume the input geometry satisfies the constraints of a Markov Random Field model, and represent the input geometry by a hierarchical distance field. This allows us to perform fast matching between a target distance field that is partially synthesized, and the input distance field. Once the target distance field is completed, we copy the original corresponding geometry elements to the synthesized result. We show that automatically generating geometry by example can be achieved within reasonable computing times, and is able to produce convincing results.
Computational Geometry
Texture Synthesis
Stochastic geometry
Distance transform
Markov random field
Complex geometry
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Computational Geometry
Convex geometry
Complex geometry
Analytic geometry
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A two-parameter constraint-based fracture mechanics approach is used to explain the effect of the constraint on the apparently anomalous behavior of short fatigue cracks. The different levels of stress constraint are quantified by the T-stress, and microstructurally as well as mechanically short cracks are discussed. Short cracks generally behave more sensitively to the constraint than the long ones. It is shown that in most cases, the existence of short cracks goes hand in hand with an intrinsic loss of the constraint, which contributes to a decrease of their fatigue threshold values and accelerates their growth. In this paper, the above effect is quantified and conclusions concerning the applicability of the fracture mechanics parameters and approaches to the estimation of the residual fatigue life of structures are discussed.
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The motion of the system with unilateral constraints being imposed may be divised into positions, so that in certain positions the constraint is taut and the motion occurs as if the constraint was bilateral and in other positions the constraint is not taut and the motion occurs as if there was no such constraint. In the present paper two problems are discussed : 1. To determine the constant of time along with the positions and the velocities of the system when the system has just been released from the constraint. 2. To write the equations of motion of the system when the system has been released from the constraint.
Constant (computer programming)
Constant of motion
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In this paper, the mathematical programs with vanishing constraints or MPVC are considered. We prove that an MPVC-tailored penalty function, introduced in [5], is still exact under a very weak and new constraint qualification. Most importantly, this constraint qualification is shown to be strictly stronger than MPVC-Abadie constraint qualification.
Penalty Method
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Polygon (computer graphics)
Computational Geometry
Containment (computer programming)
Solid geometry
Convex geometry
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