DIGITAL IMAGE PROCESSING (R18A0422)
Walsh transforms Hadamard Transform
Chapter3 Image Transforms
3.2 The Fourier Transform and Properties h bl f. • 3.3 Other Separable Image Transforms. • 3.4 Hotelling Transform. Digital Image Processing.
LECTURE NOTES ON DIGITAL IMAGE PROCESSING
For our purposes the process of sampling a 1-D signal can be reduced to three facts and a theorem. •. Fact 1: The Fourier Transform of a discrete-time signal
Distance Transformations in Digital Images
Consider a digital binary image consisting of feature and non-feature pixels. The features can be points
Lecture 2: Geometric Image Transformations
8 sept. 2005 A spatial transformation of an image is a geometric transformation of the ... A digital image array has an implicit grid.
Fundamentals of Digital Image Processing
Digital Image Processing: Problems and Applications 1. Image Representation and Modeling 4 The One-Dimensional Discrete Fourier Transform (DFT) 141.
Compression Restoration
“Compressive Sensing
CHAPTER 2 DIGITAL IMAGE TRANSFORM ALGORITHMS
I. Pitas Digital Image Processing Fundamentals. Digital Image Transform Algorithms. THESSALONIKI 1998. 2.2. Contents. ?Introduction.
The Haar–Wavelet Transform in Digital Image Processing: Its Status
The digital images may be treated as such ”spiky” signals. Unfortunately the Haar Transform has poor energy compaction for image
Need for transform 2D Orthogonal and Unitary transform and its
For most image processing applications anyone of the mathematical transformation are applied to the signal or images to obtain further information from that
Lecture 2: Geometric Image Transformations
Harvey Rhody
Chester F. Carlson Center for Imaging Science
Rochester Institute of Technology
rhody@cis.rit.eduSeptember 8, 2005
AbstractGeometric transformations are widely used for image registration and the removal of geometric distortion. Common applications include construction of mosaics, geographical mapping, stereo and video.DIP Lecture 2Spatial Transformations of Images
A spatial transformation of an image is a geometric transformation of the image coordinate system.It is often necessary to perform a spatial transformation to:•Align images that were taken at different times or with different sensors
•Correct images for lens distortion •Correct effects of camera orientation •Image morphing or other special effectsDIP Lecture 21
Spatial Transformation
In a spatial transformation each point(x,y)of imageAis mapped to a point(u,v)in a new coordinate system. u=f1(x,y) v=f2(x,y)Mapping from(x,y)to(u,v)coordinates. A digital image array has an implicit grid that is mapped to discrete points in the new domain. These points may not fall on grid points in the new domain.DIP Lecture 22Affine Transformation
An affine transformation is any transformation that preserves collinearity (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of distances (e.g., the midpoint of a line segment remains the midpoint after transformation). In general, an affine transformation is a composition of rotations, translations, magnifications, and shears. u=c11x+c12y+c13 v=c21x+c22y+c23 c13andc23affect translations,c11andc22affect magnifications, and the
combination affects rotations and shears.DIP Lecture 23Affine Transformation
A shear in thexdirection is produced by
u=x+ 0.2y v=yDIP Lecture 24Affine Transformation
This produces as both a shear and a rotation.
u=x+ 0.2y v=-0.3x+yDIP Lecture 25Affine Transformation
A rotation is produced byθis produced by
u=xcosθ+ysinθ v=-xsinθ+ycosθDIP Lecture 26Combinations of Transforms
Complex affine transforms can be constructed by a sequence of basic affine transforms. Transform combinations are most easily described in terms of matrix operations. To use matrix operations we introducehomogeneous coordinates. These enable all affine operations to be expressed as a matrix multiplication. Otherwise, translation is an exception.The affine equations are expressed as
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