orthogonal

May 16, 2023

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orthogonal

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Orthogonal Drawing

Orthogonal Drawing. Kees Visser. Overview. Introduction Orthogonal representation Flow network Bend optimal drawing. Introduction. Orthogonal drawing Given embedding Only vertical or horizontal line segments Maximum degree of 4. Introduction. Uses in VLSI circuits Minimize bends

625 views • 27 slides

Orthogonal Transforms

Orthogonal Transforms. Fourier Walsh Hadamard. Review. Introduce the concepts of base functions: For Reed-Muller, FPRM For Walsh Linearly independent matrix Non-Singular matrix Examples Butterflies, Kronecker Products, Matrices

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Orthogonal Linear Contrasts

Orthogonal Linear Contrasts. This is a technique for partitioning ANOVA sum of squares into individual degrees of freedom. Definition. Let x 1 , x 2 , ... , x p denote p numerical quantities computed from the data. These could be statistics or the raw observations.

2.2k views • 38 slides

Orthogonal matrices

Orthogonal matrices. based on excelent video lectures by Gilbert Strang, MIT http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/VideoLectures/detail/lecture17.htm Lecture 17. Orthogonality. we’ve met so far orthogonal vectors When are two vector orthogonal? orthogonal subspaces

3.1k views • 45 slides

Orthogonal Separations

Orthogonal Separations. Mark R. Schure Superon and Theoretical Separation Science Laboratory, Kroungold Analytical, Inc. Blue Bell, Pennsylvania. Joe M. Davis Dept. of Chemistry and Biochemistry Southern Illinois University at Carbondale Carbondale, Illinois. Talk Overview.

464 views • 22 slides

8.2 Orthogonal Diagonalization

8.2 Orthogonal Diagonalization. Theorem 1. The following conditions are equivalent for an (n x n) matrix P: 1. P is invertible and P -1 = P T 2. The rows of P are orthonormal. 3. The columns of P are orthonormal. Proof : (1) (2) Given P -1 = P T , PP T = I

1.11k views • 15 slides

Orthogonal Base

Orthogonal Base. Cartesian Coordinate System Unit vectors: i, j, k Normalized to each other Unique representation for each position!! Convenient! Works in general: N dimension space ANY N normalized orthogonal vectors will do!!

432 views • 13 slides

Orthogonal Range Reporting

Optimal 3-d Orthogonal Range Reporting Kasper Dalgaard Larsen Joint work with Peyman Afshani and Lars Arge. Orthogonal Range Reporting. Input: n points in d -dimensional space. Task: Build structure that reports all points inside an axis-aligned query box efficiently. Our Focus:

378 views • 20 slides

Empirical Orthogonal Functions

Empirical Orthogonal Functions. Andy Jacobson and Brad Holcombe July 2006. Variance and Covariance. Notes: E() is expectation (mean) M is the number of obs N is the number of stations (locations with data) All vectors are arranged in columns unless transposed.

293 views • 13 slides

5.1 Orthogonal Projections

5.1 Orthogonal Projections. Orthogonality. Recall: Two vectors are said to be orthogonal if their dot product = 0 (Some textbooks state this as a T b = 0) ____ The length (magnitude) of a vector is √ v · v A vector is called a unit vector if its length is 1.

925 views • 17 slides

Orthogonal moments

Orthogonal moments. Tomáš Suk. Department of Image Processing. Orthogonal moments – transformation of features. Geometric moment. Orthogonal moment. Why to use the orthogonal moments ?. Numerical precision. Why to use the orthogonal moments ?. Numerical precision. log F max

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Orthogonal Range Searching

Orthogonal Range Searching. Linear Range Search : 1-dim Range Trees 2-dimensional Range Search : kd-trees 2-dimensional Range Search : 2-dim Range Trees Range Search in Higher Dimensions. Range search. Salary. Children. Age. Input: Set of data points in d-space,

470 views • 12 slides

5.3 Orthogonal Transformations

5.3 Orthogonal Transformations. This picture is from knot theory. Recall. The transpose of a matrix. The transpose of a matrix is made by simply taking the columns and making them rows (and vice versa) Example:. Properties of orthogonal matrices (Q).

1.74k views • 26 slides

Orthogonal Range Search

Orthogonal Range Search. deBerg et. al (Chap.5). 1D Range Search. Data stored in balanced binary search tree T Input: range tree T and range [x,x ’ ] Output: all points in the range. Find split node

375 views • 21 slides

Orthogonal Transforms

Orthogonal Transforms. Fourier. Review. Introduce the concepts of base functions: For Reed-Muller, FPRM For Walsh Linearly independent matrix Non-Singular matrix Examples Butterflies, Kronecker Products, Matrices

1.04k views • 67 slides

Orthogonal Range Searching

Orthogonal Range Searching. Linear Range Search : 1-dim Range Trees 2-dimensional Range Search : kd-trees 2-dimensional Range Search : 2-dim Range Trees Range Search in Higher Dimensions. A ssumption : no two points have the same x or y coordinates. y. x. Range Trees.

342 views • 13 slides

Orthogonal Contrasts

Orthogonal Contrasts. Orthogonality. c i = 0. [c 1i x c 2i ] = 0. -1 -1 +1 +1 -- c i = 0 -1 +1 -1 +1 -- c i = 0 +1 -1 -1 +1 -- c i = 0. Calculating Orthogonal Contrasts. d.f. (single contrast) = 1. S.Sq(contrast) = M.Sq = [ c i x Y i ] 2 /nc i 2 ].

393 views • 37 slides

A = (orthogonal) (diagonal) (orthogonal)

SVD Computing. A = (orthogonal) (diagonal) (orthogonal). SVD Computing. A = (orthogonal) (diagonal) (orthogonal). 1. Find eigenvalue Decomposition for C. 2. 3. SVD Computing. Bad Idea. All zeros are destroyed. SVD Computing. Good Idea. Bidiagonal.

128 views • 5 slides

Orthogonal moments

Orthogonal moments. Legendre Zernike Fourier-Mellin Czebyshev Krawtchuk, Hahn. Two reasons for using OG moments. Avoiding numerical problems with high values, recurrent calculations Image reconstruction. Image reconstruction from geometric moments. Legendre polynomials. Definition.

283 views • 18 slides

Constructing Orthogonal Arrays

Constructing Orthogonal Arrays. Learning Objectives. • Introduce & explore orthogonality • Study the standard OAs • Practice computing DOF of an experiment • Learn how to select a standard OA • Introduce means to modify OAs • Consider studying interactions in OAs.

410 views • 31 slides

Orthogonal moments

Orthogonal moments. - set of orthogonal polynomials. Motivation for using OG moments Stable calculation by recurrent relations Easier and stable image reconstruction. Numerical stability. How to avoid numerical problems with high dynamic range of geometric moments?. Standard powers.

949 views • 89 slides

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