Kluwer - Handbook of Biomedical Image Analysis Vol

RT3D ultrasound. See Real-time three-dimensional ultrasound

Saccular (berry) aneurysms, 186, 187f Scaling

feature-based registration and, 21

retinal image registration and, 154, 157, 158, 159, 160, 163, 165, 171, 173f, 176, 177, 178

Search space, 343, 345–347 Search strategy, 343, 348–350 Seed points, 540 Segmentation

aneurysm, 193–202

atlas-based (see Atlas-based segmentation) level set (see Level set segmentation) manual, 462, 464, 471–472

multimodal, 69–70

Mumford-Shah, 56, 61–62, 66, 67, 86 registration combined with, 537 rigid, 5

shape detection, 77

volumetric (see Computer-aided volumetric segmentation)

Segmentation algorithms, 342 SEM algorighm. See Stochastic

expectation-maximization algorithm Semi-automatic registration, 7, 364–365 Semi-local models, 346

Sequential spatial filtering, 496–498 Shape-based regularizers, 57, 58 Shape detection segmentation, 77 Shape editing, 262, 263–264

Shape index, 25

Shape models, 64, 65, 454 Shape priors, 66–69 Shape spectrum, 26

Shape voxel parametrizing, 256–260 Signal-to-noise ratio, 63

Similarity index (SI), 453, 461–463, 464, 465, 466–467, 468f, 469f

Similarity measures. See also Cross-entropy; Entropy; Mutual information; Reversed cross-entropy; Symmetric divergence

in non-rigid registration, 275 in pixel-based registration, 347 in Romeo, 286

in 3D image registration, 393–427

in 3D rigid body registration, 105–106, 120–121

Similarity transformation matrix, 8–9 Simplex downhill optimization, 108, 136

binning technique and, 545, 548

retinal image registration and, 156, 162, 163–164, 165, 178

Simulated annealing, 162, 174, 176

Simulated Brain Database (SBD), 72. See also BrainWeb phantom

Single photon emission computed tomography (SPECT), 2, 3, 103, 395

elastic image registration and, 376

level set segmentation and, 63, 70, 74, 76 small animal imaging and, 535

Small animal imaging, 535–536 Smoking, 40

Snake(s), 253, 254, 436. See also Active contours; Deformable models

Snake Automatic Partitioning (SNAP), 77 Sobolev space, 345

Soft constraints, 495 Spatial elasticity tensor, 493 Spatial registration, 4

SPECT. See Single photon emission computed tomography

Spin image surface registration, 22, 26–27, 28f Spin maps, 27

Splash surface registration, 22–24

SPM spatial normalization approach, 282 Squared-error similarity functions, 225 SSD. See Sum of Squared Differences Stereo images, 342

Stereo retinal images, 156, 166, 167–168f, 169, 176, 177, 178

Stochastic expectation-maximization (SEM) algorithm, 78, 79, 289–290, 297, 300f, 301

Stopping criterion, 371

Strain energy, 353, 360, 492, 493

Strain measurement, of coronary artery, 507–512

Structural indexing, 22–24 Stunned myocardium, 512

Subarachnoid hemorrhage (SAH), 187–188 Sum of Squared Differences (SSD), 281, 282,

347, 358–359, 362f, 364, 367 Sum Rule fusion, 460 Surface(s), 12–13

free-form, 21, 22

inverse consistent registration and, 220 non-rigid registration and, 277 parametric, 13

Rational Gaussian (see Rational Gaussian surface)

Surface-based registration techniques, 21–31, 34, 538

COSMOS, 22, 24–26 point signature, 22, 24 spin image, 22, 26–27, 28f splash, 22–24

surface signature, 22, 28–31, 34 Surface signature surface registration, 22,

28–31, 34

Symmetric divergence, 394, 395–427 implementation of, 397–402 maximization of, 397, 403–405, 406–417 minimization of, 396, 405–406, 417–422 numerical stability and, 401–402, 414–417,

419–422

registration experimental set-up for, 402–406 Symmetric gradient operator, 493

Symmetric similarity cost functions, 223–225

Talairach proportional squaring system, 276 Talairach stereotaxic space, 276

Tangent stiffness, 495

Target image, 348, 487, 489, 490, 492, 503, 509 Template image, 345

data term for, 348

deformable image registration and, 487, 488, 489, 490, 491, 497, 498, 499f, 503, 506, 509, 514, 515, 517–518

Template matching, 29

Temporal retinal images, 156, 166, 167–168f, 170, 171, 176, 177, 178

Test image, 339, 340, 358

Thin-plate spline (TPS) deformations, 277–278, 316

Thin-plate spline (TPS) interpolation, 352–354 Thin-plate spline (TPS)-RPM algorithm, 278 Thin-plate spline (TPS) solutions, 348 Thin-plate spline (TPS) transformations, 124,

137

Thin-plate spline (TPS) warping, 122, 125, 128, 129, 130f, 131, 132, 133f, 134f, 135, 138, 139, 140

Three-dimensional digital subtraction angiography (DSA), 190

Three-dimensional echocardiography (3DUS), 75–76

Three-dimensional image registration, 103–142, 393–427. See also Cross-entropy; Reversed cross-entropy; Symmetric divergence; Three-dimensional non-rigid body registration; Three-dimensional rigid body registration

Three-dimensional level set segmentation, 78–88

in brain reconstruction, 79–81 of the cortex, 81–84

robust adaptive, 78–79

Three-dimensional non-rigid body registration, 104, 121–141

algorithm, 122–125

algorithmic implementation, 135–137 algorithmic robustness and efficiency, 139 applications of, 137–138, 140

evaluation of, 125–126, 138–139

examples and results, 126–128 quantitative evaluation of, 132–135 rationale for, 121–122

3D rigid body registration comparison, 129–132

Three-dimensional rigid body registration, 104, 105–123, 125, 135–136, 139, 140, 141

accuracy of, 118–119, 121–122 algorithm, 120–121

algorithm with special features, 106–108 assessment of pelvic, 112–115 assessment of procedure, 119–120 assessment of prostate, 115–116 computer implementation of, 121 consistency of, 110

evaluation of, 109–111 examples and results, 111–116 implementation issues, 117–118

3D non-rigid body registration comparison, 129–132

Thresholding outliers, 13 Threshold level set methods, 78 Time series in registration, 4 Tissue types, labeling of, 436 TPS. See Thin-plate spline Transformation(s)

affine (see Affine transformations) atlas-based segmentation and, 455–457 cross entropy, symmetric divergence, and,

399

curved (elastic), 6

deformable image registration and, 487 diffeomorphic, 221, 226

finding parameters of, 7

forward (see Forward transformations) geometric, 278, 283

global, 6, 275

ICP algorithm and, 10–11

inverse consistent (see Inverse consistent transformations)

local, 6 motion, 11, 14 nature of, 6 non-rigid, 452

pairwise consistent, 222 projective, 6 propagation of, 455–457 residual, 222

retinal image registration and, 157, 158–160

reverse (see Reverse transformations) rigid (see Rigid transformations) rotation, 11

thin-plate spline, 124, 137 translation, 11

Transformation matrix, 31 ICP algorithm and, 11 similarity, 8–9

Transformation parameterization, 227–228 Transform-based registration, 343, 344, 348 Transitivity, 231–233

Translation, 8, 9, 21

cross entropy, symmetric divergence, and, 399, 405, 415, 418f, 419, 421, 422f, 423f, 425f, 427f

genetic algorithms and, 18

level set segmentation and, 69–70

retinal image registration and, 154, 157, 158, 159, 160, 163, 165, 171, 172f, 176, 177, 178

Translation transformations, 11 Traumatic aneurysms, 186 Triangular meshes, 13

True registration, 411–414, 418–419 Tumors, 2, 3, 72, 73. See also Brain tumors Two-dimensional echocardiography (2DE),

74–75

U (energy term), 490, 491–493, 495

UL-TPS image registration. See Unidirectional thin-plate spline image registration

Ultrasound, 3 interventional, 536 intravascular, 507–512

level set segmentation and, 54, 62, 63, 67, 68, 76

RT3D (see Real-time three-dimensional ultrasound)

Unidirectional thin-plate spline (UL-TPS) image registration, 234–235, 237–245

Uzawa algorithm, 496

Variational formulation, 346, 352

Video compression, 342

Virtual springs, 364–365

Viscous fluid models, 226, 346, 488

Visible Human Project, 77 Voigt notation, 489, 494 Volume

bias from, in segmentation, 462–463 from contour to, 277–278

floating (see Floating volume)

inverse consistent registration and, 220 reference (see Reference volume)

3D non-rigid body registration and, 127 voxel-based, 21

Volume of interest (VOI), 123–125, 136–137, 138, 139

Volumetric image segmentation. See Computer-aided volumetric segmentation

Volumetric magnetic resonance imaging (MRI), 514–516

Vote Rule decision fusion, 460

Voxel-based registration, 5–6, 103–104, 122, 538 Voxel-based volumes, 21

Voxel displacement, 110–111, 117 Voxel similarity approaches, 394

W (energy term), 490, 491–493, 519 Warfield algorithm, 470

Warping, 339–340, 345, 346–347, 364, 374–375, 376. See also Hyperelastic warping; Thin-plate spline warping

Warp space. See Search space Wavelets, 227, 344, 346, 349

White matter, 71, 78, 79, 81–84, 225, 317, 542 coupling-surfaces regularizers and, 59 geometric deformable models and, 80–81 intensity correction and, 289–290 multiple sclerosis and, 36

overlap with gray matter, 313–315 White noise, 154, 354

Window levelling, 190

X-ray(s), 2, 41

X-ray fluoroscopy, 536