A ROBUST AFFINE INVARIANT METRIC ON BOUNDARY PATTERNS

1999 ◽  
Vol 13 (08) ◽  
pp. 1151-1163 ◽  
Author(s):  
MICHIEL HAGEDOORN ◽  
REMCO C. VELTKAMP
Keyword(s):  
Algebraic Surface ◽  
Shape Recognition ◽  
Large Family ◽  
Finite Union ◽  
Connected Components ◽  
Affine Invariant ◽  
Invariant Metric ◽  
Pattern Metrics ◽  
Surface Patches

Affine invariant pattern metrics are useful for shape recognition. It is important that such a metric is robust for various defects. We formalize these types of robustness using four axioms. Then, we present the reflection metric. This is an affine invariant metric defined for the large family of "boundary patterns". A boundary pattern is a finite union of n-1 dimensional algebraic surface patches in ℝn. Such a pattern may have multiple connected components. We prove that the reflection metric satisfies the four robustness axioms.

When is a Distribution of Signs Locally Completable?

1994 ◽  
Vol 46 (3) ◽  
pp. 449-473 ◽  
Author(s):  
F. Acquistapace ◽  
F. Broglia ◽  
E. Fortuna
Keyword(s):  
Algebraic Curve ◽  
Algebraic Surface ◽  
Regular Function ◽  
Connected Components ◽  
Semialgebraic Sets ◽  
Sign Distribution

AbstractLet V be an irreducible nonsingular algebraic surface, Y ⊂ V be an algebraic curve and P a point of Y. Suppose a sign distribution is given locally in a neighbourhood of P on some connected components of V — Y. We give an algorithmic criterion to decide whether this sign distribution is induced by a regular function or not. As an application, this criterion enables one to decide whether two semialgebraic sets can be locally separated or not.

C1 MODELING WITH HYBRID MULTIPLE-SIDED A-PATCHES

2002 ◽  
Vol 13 (02) ◽  
pp. 261-284
Author(s):  
GUOLIANG XU ◽  
CHANDRAJIT L. BAJAJ ◽  
SUSAN EVANS
Keyword(s):  
Algebraic Surface ◽  
Degrees Of Freedom ◽  
Real Zero ◽  
Rational Functions ◽  
Rational Form ◽  
Surface Patches

We propose a new scheme for modeling a smooth interpolatory surface, from a surface discretization consisting of triangles, quadrilaterals and pentagons, by algebraic surface patches which are subsets of real zero contours of trivariate rational functions defined on a collection of tetrahedra and pyramids. The rational form of the modeling function provides enough degrees of freedom so that the number of the surface patches is significantly reduced, and the surface has quadratic recover property.

scholarly journals Synthesized affine invariant function for 2D shape recognition

2007 ◽  
Vol 40 (7) ◽  
pp. 1921-1928 ◽  
Author(s):  
Wei-Song Lin ◽  
Chun-Hsiung Fang
Keyword(s):  
Shape Recognition ◽  
Invariant Function ◽  
Affine Invariant

scholarly journals EFFICIENT ORIENTATION AND CALIBRATION OF LARGE AERIAL BLOCKS OF MULTI-CAMERA PLATFORMS

2016 ◽  
Vol XLI-B1 ◽  
pp. 199-204
Author(s):  
W. Karel ◽  
C. Ressl ◽  
N. Pfeifer
Keyword(s):  
Data Management ◽  
Positive Impact ◽  
Feature Point ◽  
Affine Invariant ◽  
Self Calibration ◽  
Surface Patches ◽  
Bundle Block Adjustment ◽  
Similarity Invariant ◽  
Feasible Solutions

Aerial multi-camera platforms typically incorporate a nadir-looking camera accompanied by further cameras that provide oblique views, potentially resulting in utmost coverage, redundancy, and accuracy even on vertical surfaces. However, issues have remained unresolved with the orientation and calibration of the resulting imagery, to two of which we present feasible solutions. First, as standard feature point descriptors used for the automated matching of homologous points are only invariant to the geometric variations of translation, rotation, and scale, they are not invariant to general changes in perspective. While the deviations from local 2D-similarity transforms may be negligible for corresponding surface patches in vertical views of flat land, they become evident at vertical surfaces, and in oblique views in general. Usage of such similarity-invariant descriptors thus limits the amount of tie points that stabilize the orientation and calibration of oblique views and cameras. To alleviate this problem, we present the positive impact on image connectivity of using a quasi affine-invariant descriptor. Second, no matter which hard- and software are used, at some point, the number of unknowns of a bundle block may be too large to be handled. With multi-camera platforms, these limits are reached even sooner. Adjustment of sub-blocks is sub-optimal, as it complicates data management, and hinders self-calibration. Simply discarding unreliable tie points of low manifold is not an option either, because these points are needed at the block borders and in poorly textured areas. As a remedy, we present a straight-forward method how to considerably reduce the number of tie points and hence unknowns before bundle block adjustment, while preserving orientation and calibration quality.

Affine-invariant Shape Recognition Using Grassmann Manifold

2012 ◽  
Vol 38 (2) ◽  
pp. 248-258 ◽  
Author(s):  
Yun-Peng LIU ◽  
Guang-Wei LI ◽  
Ze-Lin SHI
Keyword(s):  
Grassmann Manifold ◽  
Shape Recognition ◽  
Affine Invariant ◽  
Invariant Shape
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