Digital image warping

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Adaptive supersampling, 169

Affine transformation, 47-51

incremental, 193

inferring, 50-51

inverse, 50

Aliasing, 8, 106-108

Analog-to-digital converter, 31

Antialiasing, 8, 108-111

Area sampling, i66

Bandlimited function, 97

Bartlett window, 128

Baseband, 99


interpolation, 58

inverse, 60

mapping, 57

separability, 59

transformation, 57-61

Blackman window, 140

Blinn, 178

Bottleneck, 219

Boult, 88, 242

Boundary conditions, 289

Box filter, 126

Braccini, 205

Briggs, 221

B-splines, 134-137

Butterfly flow graph, 269

Catmull, 178,206, 215

CCD camera, 32, 35


Chateau function, 128

CID camera, 32, 36

Comb function, 30

Control points, 63, 133

Convolution, 16-18

Convolution kemel 16

Cook, 178

Cooley-Sande algorithm, 276

Cooley-Tukey algorithm, 274

CORDIC algorithm, 185, 212-214

Coueignoux, 179

Cubic convolution, i29

Cubic splines, 133,283-296

Danielson-Lanczos lemma, 267

Decimation-in-frequency, 276

Decimation-in-time, 274

Digital image, 12

Digital image acquisition} 28

Digitization, 31

Digitizers, 28

Dirac delta function, 15

Discrete image, 12

Discrete Fourier transfom, 26-28,266

Dram scanner, 36

Elliptical weighted average filter, 179

Exponential filters, 145-146

Fant, 153

Feibush, 178

FFT, 28, 265-282

Filter, 14


ff 7r ii

316 INozx

finite impulse response, 125

infinite impulse response, 125

kernel, i6

linear, i4

low-pass, 100

mcursive, 125

response, 14

space-invariant, 14, 168

space-variant, 168

Flat-bed scanners, 36

Flying spot scanner, 32

Foldover, 220

Forward difference, 199, 297-300

Forward mapping, 42, 188

Four-comer mapping, 43


coefficients, 22

integral, 23

series, 22

transfom, 20-26

properties, 25-26

spectrum, 21

window, 126

Frame buffer, 38

Frame grabber, 38

Frame store, 38

Fraser, 22i

Frequency domain, 19

Frequency leakage, 104

Frozen edge, 228

Gangnet, 179

Gaussian window, I43

Geometric transfomation, 1

Gibbs phenomenon, 22, 102

Global splines, 81-84

Global transfommtion, 76

Gouraud shading, 190

Gray levels, 12

Greene, 179

Grimson, 85

Ground control points, 63

Hamming window, 139

Hann window, 139

Heckbert, 179

Homogeneous coordinates, 46-47

Image, 11

continuous, 12

continuous-continuous, 12

continuous-discrete, 12

discrete-continuous, 12

discrate-discrete, 12

dissectors, 34-35

element, 31

reconstruction, 7, 17, 95, 99-105, 117

registration, 2

resampling, 7, 117

Impulse response, 15

Incremental algorithms, 189

Interpolation, 124

Interpolation grid, 60-61, 63

Interpolation kernels, 126-146

Inverse mapping, 44, i88

Irregular sampling, 173

Jittered sampling, 175

Kaiser window, 141

Kender, 88

Kronecker delta function, 15

Lanczos window, 142

Least Squares

Ordinary Polynomials, 65-67

Orthogonal Polynomials, 67-70

Weighted, 70-75

Levoy, 178

Linear interpolation, 127

Local transformation, 77

Marino, 205

Mesh warping, 222-240

Microdensitometer, 37

Mip maps, 181

Monochrome image, 12

Multispectral image, 12

Nearest neighbor, 126

Newell, 178

Normal equations, 66

NTSC, 37

Nyquist rate, 99

Paeth, 208

PAL, 37

Parzen window, 135

Passband, 103

Pel, 31

Pemy, 179

Perspective transformation, 52-56

incremental, 196

Inferring, 53-56

Inverse, 52

Robertson, 240

Two-pass, 218

Picture element, 31

Piecewise polynomial transformations, 75-81

Pixel, 7, 31

Point diffusion, 176

Point sampling, 8, 96, i63

Point shift algorithm, 126

Point spread function, 16, 29

Poisson-disk distribution, 174

Poisson sampling, 174

Polynomial transfmations, 61-75

Postaliasing, 108

Postfilter, 108

Prealiasing, 108

Prefilter, 108, 166, 181

Preimage, 166

Pseudoinverse solution, 64-65

Pyramids, 181

Quantization, 30-31

Rate buffering, 38

Reconstruction, 17, 95, 99-105, 1 i7

Regularizafion, 84

Regular sampling, 168

Resampling filter, 121

Robertson, 240

Roof function, 128

Rotation, 49, 205-214

Sample-and-hold function, 126

Sampling, 12, 97-98

Adaptive, 169

Area, 166

irregular, 173

jittered, 175

nonunifoma, 173

point-diffusion, 176


regular, 168

Poisson, 174

stochastic, 173

uniform, 168

Sampling grid, 7, 30, 117

Sampling theory, 6, 95-116

Scale, 49

Scanline algorithms, 9, 187

Scanning camera, 36

Schowengerdi, 221

Screen space, 178


Separability, 29, 59, 187, 214

Separable mapping, 188,240

Shear, 49

Sifting integral, 15

Signal, 11

Sinc function, 101-102

Smith, 206, 215,221


domain, 19

interpolation, 63

transformation, 6, 41-94

Special Effects, 222

Stochastic sampling, 173

Stopband, 103

Summed-area tables, 183

Supersampling, 168

Surface fitting, 75, 81

Tanaka, 208

Tent filter, 128

Terzopoulos, 86

Texture mapping, 189

Texture space, 178

Tiepoints, 63

Transfomation matrix, 45

Translation, 48

Triangle filter, 128

Triangulation, 78-81

Two-parameter cubic filter, 131

Unifom sampling, 168

Video digitizer, 37

Vidicon camera, 32-34

Warp, 1


318 lsox

Weiman, 206

Windowed sine function, 137-146


Blackman, 140

Gaussian, 143

Hamming, 139

Hann, 139

Kaiser, 141

Lanczos, 142

Rect, 137

Wolberg, 241-242



George Wolberg was born on February 25, 1964, in Buenos Aires, Argentina. He

received the B.S. and M.S. degrees in electrical engineering from Cooper Union, New

York, NY, in 1985, and the Ph.D. degree in computer science from Columbia University,

New York, NY, in 1990.

He is currently an Assistant Professor in the Computer Science deparanent at the

City College of New York / CUNY, and an Adjunct Assistant Professor at Columbia

University. He has worked at AT&T Bell Laboratories, Murray Hill, NJ, and at IBM T.J.

Watson Research Center, Yorktown Heights, NY, during the summers of 1983/4 and

1985/9, respectively. His research at these labs centered on image restoration, image

segmentation, graphics algorithms, and texture mapping. From 1985 to 1988, he served

as an image processing consultant to Fantastic Animation Machine, New York, NY, and

between 1986 and 1989, he had been an Instructor of Computer Science at Columbia

University. He spent the summer of 1990 at the Electrotechnical Laboratory in Tsukuba,

Ibaraki, Japan, as a selected participant in the Summer Institute in Japan, a research pro-

gram sponsored by the U.S. National Science Foundation and by the Science and Tech-

nology Agency of Japan.

Dr. Wolberg was the recipient of a National Science Foundation Graduate Fellow-

ship. His research interests include image processing, computer graphics, and computer

vision. He is a member of Tau Beta Pi, Eta Kappa Nu, and the IEEE Computer Society.

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