Results 1  10
of
7,476
Transformations of surface normal vectors
 Tech. Rep. 22, Apple Computer
, 1990
"... Abstract: Given an affine 4x4 modeling transformation matrix, we derive the matrix that represents the transformation of a surface’s normal vectors. This is similar to the modeling matrix only when any scaling is isotropic. We further derive results for transformations of light direction vectors and ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract: Given an affine 4x4 modeling transformation matrix, we derive the matrix that represents the transformation of a surface’s normal vectors. This is similar to the modeling matrix only when any scaling is isotropic. We further derive results for transformations of light direction vectors
New Computation of Normal Vector and Curvature
"... Abstract: The local geometric properties such as curvatures and normal vectors play important roles in analyzing the local shape of objects. The result of the geometric operations such as mesh simplification and mesh smoothing is dependent on how to compute the normal vectors and the curvatures of ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract: The local geometric properties such as curvatures and normal vectors play important roles in analyzing the local shape of objects. The result of the geometric operations such as mesh simplification and mesh smoothing is dependent on how to compute the normal vectors and the curvatures
A tutorial on support vector machines for pattern recognition
 Data Mining and Knowledge Discovery
, 1998
"... The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SV ..."
Abstract

Cited by 3393 (12 self)
 Add to MetaCart
The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when
Gene selection for cancer classification using support vector machines
 Machine Learning
"... Abstract. DNA microarrays now permit scientists to screen thousands of genes simultaneously and determine whether those genes are active, hyperactive or silent in normal or cancerous tissue. Because these new microarray devices generate bewildering amounts of raw data, new analytical methods must ..."
Abstract

Cited by 1115 (24 self)
 Add to MetaCart
available training examples from cancer and normal patients, we build a classifier suitable for genetic diagnosis, as well as drug discovery. Previous attempts to address this problem select genes with correlation techniques. We propose a new method of gene selection utilizing Support Vector Machine methods
An approximation for Normal Vectors of Deformable Models
"... Abstract. A physicallybased deformable model proposed by Terzopoulous et al. is governed by the Lagrange’s form, that establishes the relation between the dynamics of deformable models under the influence of applied forces. The net instantaneous potential energy of deformation is derived on the bas ..."
Abstract
 Add to MetaCart
on the basis of the geometric properties, namely the first and second fundamental forms. For simplicity, the normal vector at each sample point is approximated by the second derivative. In this paper we present another approximation for the normal vector which offers better visual simulation. Some comparisons
Asymptotically Normal Vectors by
, 2007
"... Abstract We obtain the Edgeworth expansion for P(n 1/2 ( ˆ θ − θ) < x) and its derivatives, and the tilted Edgeworth (or saddlepoint or small sample) expansion for P ( ˆ θ < x) and its derivatives where ˆθ is any vector estimate having the standard cumulant expansions in powers of n −1. ..."
Abstract
 Add to MetaCart
Abstract We obtain the Edgeworth expansion for P(n 1/2 ( ˆ θ − θ) < x) and its derivatives, and the tilted Edgeworth (or saddlepoint or small sample) expansion for P ( ˆ θ < x) and its derivatives where ˆθ is any vector estimate having the standard cumulant expansions in powers of n −1.
Support Vector Machine Classification and Validation of Cancer Tissue Samples Using Microarray Expression Data
, 2000
"... Motivation: DNA microarray experiments generating thousands of gene expression measurements, are being used to gather information from tissue and cell samples regarding gene expression differences that will be useful in diagnosing disease. We have developed a new method to analyse this kind of data ..."
Abstract

Cited by 569 (1 self)
 Add to MetaCart
using support vector machines (SVMs). This analysis consists of both classification of the tissue samples, and an exploration of the data for mislabeled or questionable tissue results. Results: We demonstrate the method in detail on samples consisting of ovarian cancer tissues, normal ovarian tissues
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
Abstract

Cited by 568 (10 self)
 Add to MetaCart
We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
Rendering of Surfaces from Volume Data
 IEEE COMPUTER GRAPHICS AND APPLICATIONS
, 1988
"... The application of volume rendering techniques to the display of surfaces from sampled scalar functions of three spatial dimensions is explored. Fitting of geometric primitives to the sampled data is not required. Images are formed by directly shading each sample and projecting it onto the picture ..."
Abstract

Cited by 875 (12 self)
 Add to MetaCart
the picture plane. Surface shading calculations are performed at every voxel with local gradient vectors serving as surface normals. In a separate step, surface classification operators are applied to obtain a partial opacity for every voxel. Operators that detect isovalue contour surfaces and region
Discrete DifferentialGeometry Operators for Triangulated 2Manifolds
, 2002
"... This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Vorono ..."
Abstract

Cited by 449 (14 self)
 Add to MetaCart
This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging
Results 1  10
of
7,476