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On Pencils of Tangent Planes and the
"... This paper presents a geometric approach to recognizing smooth objects from their outlines. We define a signature function that associates feature vectors with objects and baselines connecting pairs of possible viewpoints. Feature vectors, which can be projective, a#ne, or Euclidean, are compute ..."
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, are computed using the planes that pass through a fixed baseline and are also tangent to the object's surface. In the proposed framework, matching a test outline to a set of training outlines is equivalent to finding intersections in feature space between the images of the training and the test
Tangent Line and Tangent Plane Approximations of Definite Integrals
"... Abstract. Oftentimes, it becomes necessary to find approximate values for definite integrals, since the majority cannot be solved through direct computation. The methods of tangent line and tangent plane approximation can be derived as methods of integral approximation in two and threedimensional ..."
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Abstract. Oftentimes, it becomes necessary to find approximate values for definite integrals, since the majority cannot be solved through direct computation. The methods of tangent line and tangent plane approximation can be derived as methods of integral approximation in two and three
Variational Tangent Plane Intersection for Planar Polygonal Meshing
"... Abstract. Several theoretical and practical geometry applications are based on polygon meshes with planar faces. The planar panelization of freeform surfaces is a prominent example from the field of architectural geometry. One approach to obtain a certain kind of such meshes is by intersection of s ..."
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of suitably distributed tangent planes. Unfortunately, this simple tangent plane intersection (TPI) idea has a number of limitations. It is restricted to the generation of hexagondominant meshes: as vertices are in general defined by three intersecting planes, the resulting meshes are basically duals
Estimation of Tangent Planes for Neighborhood Graph Correction
"... Abstract. Local algorithms for nonlinear dimensionality reduction [1], [2], [3], [4], [5] and semisupervised learning algorithms [6], [7] use spectral decomposition based on a nearest neighborhood graph. In the presence of shortcuts (union of two points whose distance measure along the submanifold ..."
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the submanifold is actually large), the resulting embbeding will be unsatisfactory. This paper proposes an algorithm to correct wrong graph connections based on the tangent subspace of the manifold at each point. This leads to the estimation of the proper and adaptive number of neighbors for each point
A Restricted Genetic Algorithm Based on Ascending of Tangent Planes
"... Classical Genetic Algorithms（CGAs）accomplish the global search by selection, crossover and mutation. It has many shortages. Here we proposed a restricted genetic algorithm based on ascending of tangent plane (RGAATP). Our algorithm is simple and effective, which approaches the global solution step b ..."
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Classical Genetic Algorithms（CGAs）accomplish the global search by selection, crossover and mutation. It has many shortages. Here we proposed a restricted genetic algorithm based on ascending of tangent plane (RGAATP). Our algorithm is simple and effective, which approaches the global solution step
Projecting an Arbitrary Latitude and Longitude onto a Tangent Plane
 Online]. Available: http://www.mers.byu.edu/docs/reports/MERS9904.pdf
, 1999
"... In working with points on the Earth's surface, it is convenient at times to work with points on dened on a locally tangent plane rather than in latitude and longitude. An example of such at time is in calculating the area of a region on the ground that is small enough that the curvature of the ..."
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In working with points on the Earth's surface, it is convenient at times to work with points on dened on a locally tangent plane rather than in latitude and longitude. An example of such at time is in calculating the area of a region on the ground that is small enough that the curvature
Overcoming noise, avoiding curvature: Optimal scale selection for tangent plane recovery
 In Proceedings of IEEE Conference on Statistical Signal Processing
, 2012
"... Constructing an efficient parametrization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parametrization using the local tangent plane. Principal component analysis (PCA) is often the ..."
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Cited by 2 (2 self)
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Constructing an efficient parametrization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parametrization using the local tangent plane. Principal component analysis (PCA) is often
Improved Generalization in Recurrent Neural Networks Using the Tangent Plane Algorithm
"... Abstract—The tangent plane algorithm for real time recurrent learning (TPARTRL) is an effective online training method for fully recurrent neural networks. TPARTRL uses the method of approaching tangent planes to accelerate the learning processes. Compared to the original gradient descent real tim ..."
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Abstract—The tangent plane algorithm for real time recurrent learning (TPARTRL) is an effective online training method for fully recurrent neural networks. TPARTRL uses the method of approaching tangent planes to accelerate the learning processes. Compared to the original gradient descent real
Submitted to the Annals of Statistics OPTIMAL TANGENT PLANE RECOVERY FROM NOISY MANIFOLD
"... Constructing an efficient parametrization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parametrization using the local tangent plane. Principal component analysis (PCA) is often th ..."
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Constructing an efficient parametrization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parametrization using the local tangent plane. Principal component analysis (PCA) is often
Results 1  10
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