Index

    • a
    • affine transformation  18
    • aliasing  110
    • aspect ratio  6
    • autocorrelation  195–196
      • exponential  197, 200–201
      • matrix‐valued  197
      • properties  198
    • autocovariance  195–196
      • matrix‐valued  197
    • b
    • bandpass filter  220
    • bandstop filter  220
    • Bayer color filter array  42, 111, 181–188
    • binary operation  313
    • black space  137
    • blur, uniform out‐of‐focus  21
    • brightness  147
    • c
    • cascade of systems  15
    • change of primaries  138–140
    • chromaticity coordinates  150
    • chromaticity diagram  150
    • CIE see Commission international de l'éclairage (CIE)
    • CIELAB  155–156
    • CIE 1924 relative luminous efficiency 148
    • CIE standard observer  140–142
    • circ function  7–8
    • circularly symmetric signal  13
    • color, definition  130
    • color coordinates  147
      • change of color coordinates function  164
      • CIELAB  155–156
      • display referred  157–158
      • linear  153
      • luma‐color‐difference  158
      • luminance/chromaticities  151
      • perceptually uniform  155–156
      • sRGB  157
    • color filter array (CFA)  180
    • color matching functions  134
      • CIE 1931 RGB primaries 141
      • CIE 1931 XYZ primaries 142
      • EIZO CRT phosphor primaries  144
    • color mosaic display  188–191
    • color peak signal‐to‐noise ratio (CPSNR)  178
    • color root mean square error (CRMSE)  178
    • color vector space  135–137
      • basis  137–138
      • dimension  136–137
    • Commission international de l'éclairage (CIE)  140
    • complete symmetry group images(Λ)  256
    • complex exponential sinusoidal signal  9
    • complexification of a vector space  168
    • convolution
      • continuous domain  21
      • continuous domain, periodic  95
      • discrete domain  52
      • discrete domain, periodic  72
      • integral  21
    • coset  69, 296, 314
      • of a subspace  317
    • coset representative  70, 71, 297, 314
    • cross‐correlation  199
    • cross‐covariance  199
    • cross spectrum  201
    • d
    • DC Gain  62
    • determinant of a lattice see lattice, determinant
    • dihedral group  257, 260, 268
    • Dirac delta  12
      • periodic  94
    • directional derivative  34
    • direct sum of vector subspaces  316
    • discrete cosine transform (DCT)  276
      • one‐dimensional  276–279
      • one‐dimensional DCT‐1  276–278
      • one‐dimensional DCT‐2  278–279
      • two‐dimensional DCT‐2  279–280, 283–284, 286–287
    • discrete Fourier transform (DFT)
      • D‐dimensional rectangular  77
      • one‐dimensional  76–77
    • display aperture  112, 188
    • downsampling  237, 245–248
      • operator  245
      • system  245
    • e
    • elementary column operations  299–300
    • equivalence class  311
    • equivalence relation  311
    • Euclidean Group E(D)  255
    • expectation  195
    • f
    • fast Fourier transform (FFT)  85
    • finite impulse response (FIR) filter  59, 215–235
      • least‐pth design  229–232
      • optimization design  229–232
      • window design  226–229
    • Fourier‐Poisson cube  116–117
    • frequency response
      • continuous domain  22
      • continuous domain, color  168–170
      • discrete domain  52
      • discrete domain, color  174–175
    • fundamental domain  267
    • fundamental parallelepiped see unit cell, fundamental parallelepiped
    • g
    • gamma correction  157
    • Gaussian filter
      • FIR  217–218
      • S‐CIELAB model  171–172, 177–178
    • Gaussian probability density  196
    • Gaussian signal  10
    • gradient  25
    • Grassmann's laws  130–132
    • group  313–314
      • Abelian  313
      • subgroup  313–314
    • h
    • Hermite normal form  300–302
    • holohedry images(Λ)  256
    • i
    • impulse response  21
      • color LSI system  166–167
    • index of a sublattice  69, 296
    • inner product  317
    • interlaced scanning  47, 308
    • inversion  255, 256
    • irradiance  126
    • isometry  255
    • isotropic signal  13
    • isotropy subgroup  275
    • l
    • Laplacian of Gaussian (LoG) filter  35
    • Laplacian system  20, 34
    • lattice  42–46, 289–310
      • basis  43, 289
      • basis transformation  298–304
      • definition  43, 289
      • determinant  44, 292
      • intersection  304–306
      • properties  44, 293
      • reciprocal  49, 294–295
      • sum  306
      • symmetry of  255–256
    • least‐pth optimization  229–232
    • light, visible  125
    • linear combination  315
    • linear independence  316
    • linear shift‐invariant (LSI) system
      • continuous domain  19
      • continuous domain, color  166
      • continuous domain, periodic  94
      • discrete domain  51
      • discrete domain, color  173–174
      • discrete domain, periodic  72
    • linear system
      • continuous domain  15
      • continuous domain, color  166
      • continuous domain, periodic  94
      • discrete domain  51
    • linear transformation  316–317
      • kernel (or null space)  317
    • local frequency  11
    • low‐pass filter  216, 217
    • LSI see linear shift‐invariant (LSI) system
    • luma  158
    • luminance  147–149
      • relative  149
    • m
    • mean  195–196
      • vector‐valued  197
    • memoryless system  166
    • metameric class  130
    • metameric equivalence  130, 132–134
      • extended  135
    • metamerism  130
    • moving average filter  215–218
    • multidimensional Fourier transform, continuous domain  22
      • properties  23–27
    • multidimensional Fourier transform, continuous domain color  170
    • multidimensional Fourier transform, continuous domain periodic  96
      • inverse  118–119
      • properties  96–100
    • multidimensional Fourier transform, discrete domain  52
      • inverse  117–118
      • periodicity  52
      • properties  53–57
    • multidimensional Fourier transform, discrete domain periodic  73
      • inverse  75–76
      • periodicity  73
      • properties  77–80
    • multidimensional Nyquist sampling theorem  110
    • n
    • neutral element of a group  313
    • norm  318
    • o
    • orbit  264, 271
    • orbit representatives  264, 271
    • orientation of xy axes  6
    • orthogonal basis  317
    • orthogonal group O(D)  256
    • orthogonal matrix  256, 260
    • orthogonal vectors  317
    • orthonormal basis  318
    • p
    • Parseval relation, continuous domain  27
    • periodic signal
      • continuous domain  93
      • discrete domain  69
    • periodization  113–114
    • periodogram  207
    • physical light stimuli  128
      • set of (images)  128
    • physically realizable colors  137, 144–147
    • picture height (ph)  5
    • pixel height (px)  48
    • point group images(Λ)  256
    • Poisson summation formula  114–116
    • polynomial interpolation  251–254
    • power density spectrum, WSS random field  199–200
      • properties  200
    • power density spectrum of light  126
    • primaries, color  131, 137
      • CIE 1931 RGB 141
      • CIE 1976 Uniform Chromaticity Scale (UCS) 143
      • CIE 1931 XYZ 141–142
      • EIZO CRT RGB phosphors  144
      • ITU‐R Rec BT.709, sRGB  153–155
      • transformation of  138–140
      • Zhang‐Wandell opponent  171
    • q
    • quotient group  70, 298, 314
    • quotient space  317
    • r
    • radiance  126
    • radiant exitance  126
    • radiant flux  126
    • radiant intensity  126
    • radiometry  125
    • random field  193–195
      • wide‐sense stationary (WSS)  196
    • reciprocal basis  294
    • reciprocal lattice see lattice, reciprocal
    • rect function  7–8
    • reference white  137
    • reflectance  126
    • relative luminous efficiency  148
    • s
    • sampling  107
      • color signal, different structures  180–188
      • color signal, single lattice  175
      • ideal  107
      • practical  110–112
      • WSS random field  206
    • sampling aperture  111
    • sampling density  44, 292
    • sampling matrix  43, 290
    • sampling structure  46–47
      • conversion  237–254
      • conversion system  249
    • S‐CIELAB error criterion  175–180
    • S‐CIELAB‐PSNR  178
    • separable filters  66
    • separable function  13
    • shift system, continuous domain  16, 19
    • shift system, discrete domain  51
    • sifting property  20
    • signal space
      • color  164, 173
      • continuous domain  14
      • discrete domain  48
    • singularities  12
    • sinusoidal signal
      • continuous domain  7–10
      • continuous domain, color  168
      • continuous domain, periodic  94
      • discrete domain  49–50
      • discrete domain, color  174
      • discrete domain, periodic  71
    • Smith‐MacMillan normal form  304–305
    • Smith normal form  75, 82, 302–304
    • spatial CIELAB (S‐CIELAB) model  171
    • spatial frequency  8
    • spatial window  5–6
    • spectral density matrix  201–202
      • estimation  207–210
    • still image  5
    • structure tensor  34
    • sublattice  69, 237–239, 295–296
    • superlattice  238, 295
    • symmetry  255
    • symmetry group images(Λ)  256
      • complete see complete symmetry group images(Λ)
    • symmetry‐group invariant system  258
      • periodic  271–272
    • symmetry invariance  255
    • system
      • continuous domain  15
      • continuous domain, color signals  166
      • discrete domain  51
      • discrete domain, color signals  173
    • t
    • time‐varying image  5
    • translation transformation  256
    • tristimulus values  137–138
    • u
    • unimodular integer matrix  291
    • unit cell  44, 291–293
      • fundamental parallelepiped  292
      • Voronoi  44, 292–293
    • unit of spatial distance  5
    • unit sample response  51
      • color LSI system  174
    • upsampling  237, 239–245
      • zero‐insertion upsampler  240
    • w
    • white noise  196, 200
    • window  207, 226–227
      • Blackman‐Harris  208
      • Hamming  228
    • WSS see random field, wide‐sense stationary (WSS)
    • x
    • xy coordinate system  6
    • z
    • zero‐insertion upsampler see upsampling, zero‐insertion upsampler
    • zero‐one functions  7–8
    • zero‐phase filter  62
    • zone plate  10–12
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