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(b) PLATE 2.1: L-band synthetic aperture radar (SAR) image of ice floes in the ocean: (a) original image, 512 x 512 (pixel resolution is about 4m x 4m), (b) evolution of segmentation via stochastic relaxation with constraints; shown are sixteen "snapshots" from sixty sweeps (every third sweep) of stochas- tic relaxation (upper left panel shows the random starting configuration of edges, and the lower right panel shows the final configuration of the bound- aries). Reprinted, by permission, from Geman et al. (1990~. Copyright (I) 1990 by Institute of Electrical and Electronics Engineers.

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11i~ PLATE 2.2: Collage composed of nine Brodatz textures: leather, grass, and pigskin (top row), raffia, wool, and straw (middle row), and water, wood, and sand (bottom row). Two of the textures, leather and water, are repeated in the two circles; (a) original image 384 x 384, individual textures all 128 x 128; (b) estimated boundaries via deterministic (left panel) and stochastic (right panel) algorithms. Reprinted, by permission, from Geman et al. (1990~. Copyright (I) 1990 by Institute of Electrical and Electronics Engineers.

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(a) (b) PLATE 2.3: Single photon emission computer tomography (SPECT) recon- struction of a slice of a human skull across the eyes, from real (hospital) data: (a) filtered back projection (FBP) reconstruction, (b) reconstruction via the iterative conditional expectations (ICE) algorithms using ,B = 2.7, the ML estimator. Note that in (b) one can distinguish details such as nose bone, eyes, and brain, most of which cannot be distinguished in (a). (a) (c) (b) PLATE 2.4: SPECT reconstruction of a sim- ulated phantom. The mode} used in this experiment was developed by the Nuclear Medicine Department of the University of Massachusetts Medical Center, Worcester. This is a comprehensive model that captures the effects of photon scattering, photon atten- uation, camera geometry, and quantum noise: (a) original phantom, (b) FBP reconstruction, (c) ICE reconstruction with ,l] = 1.

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(a) :: ...... (b) ^..,~.......... . . . ............ ...... (d) ...< .... ;.t PLATE 2.5: SPECT reconstruction of a human liver/spleen scan, from real (hospital) data: (a) FBP reconstruction, (b) ICE reconstruction with ~ = 3, the ME estimator, (c) ICE reconstruction with ,0 = 0, (~) ICE reconstruction with ,B = 20; (c) and (~) demonstrate the significance of the parameter ,B (see text).

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(a) (c) (b) (d) PLATE 2.6: A shape-from-shading experiment with an egg image under uncontrolled illumination. The surface of the egg was assumed to be Lam- bertian with unknown albedo; the algorithm (a combination of constrained annealing and iterative conditional modes (ICM)) estimated, in addition to the configuration N of unit normals, the albedo p of the egg (and of the background) and an effective light source direction S: (a) original image, 64 x 64, (b) reconstruction (simultaneous estimation of N. p, and S), (c) re- constructed scene illuminated from the x-direction, (d) reconstructed scene illuminated from the y-direction.

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Area ~+ ~ (a) a ~ (C) a . (b) (d) PL0E 3]: (a) HAIR Bad 2 (credo) with clouds shown as white. (b) WHIR band 4 OnG=ed temperatures dark gray scales me ~arm. (c) Seg- mented large produced fly the PCTS~C gorgon. (d) Flag cloud-~sked large (clouds ad lad are Black) produced by the PC1S~C ~gorRhm. De- t~ls of the Ailment gray scale maps used in the panels of Plate 3.1 are given in the text.

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(b) PLATE 3.2: (a) One-half cycle of the image sequence constructed by super- position of an image of an inclined plane with that of a circle. Note, the circle is out of phase with the inclined plane and the range of data in the inclined plane is about twice that of the circle. (b) Dominant patterns of variance determined from the EOF analysis of the image sequence.

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TIME I 1 23W 9.9 - C 14.5 12.7 (a) TIME 3 123W at., 9.9 - 12.7 (C) TIME 2 123W 9 9 - C 12.7 (b) 36N 14.5 ::~ }A 36N :: 14.7 PLATE 3.3: Image sequence and geographi- cal information of a coastal filament observed oh central California by the Advanced Very High Resolution Radiometer on the polar- orbiting NOAA-9 and -10 satellites. ]:ndivid- ual gray scale mappings were used to opti- mize feature recognition. The lower temper- ature ranges (i.e., 9.9-12.7C for time step 1) were mapped to a single gray scale. (Wall! and Simpson, 1990b)

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123W 1 1 123W -37N _ - 36N (a) 123W 1 (b) 123W - 36N 1 (C) 45.0 cms~ (d) 1 37N 36N -37N -36N PLATE 3.4: (a) Edge maps. (b) Total velocity field from pattern-matching. (c) The MU normal component of velocity. (a) The tangential component of velocity computed as a difference of (b) and (c) for time step 2 of the image sequence shown in Plate 3.3. (Wahl and Simpson, l990b)

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O A) (_f.: on lo o on on, ~~ To to = (b) C) ~.~ PLATE 3.5: (a) A polar I`andsat image showing ice floes as light gray structures against a dark background. (b) The corresponding distribution, size, and shape of the ice floes. Reprintecl, by permission, from Banfield and Raftery (1989~. Copyright (I) 1989 by University of Washington.

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:: :::: - :~: ::: ~ ^~ : ::~ ~ ~ ~ ~ e A, . ~ ~ ~ ~ : ~ ~ ~ ' ~ ~ ~ O .. . : '.7.' in- '1 ': ~ tt ~ 2 ~ PLATE 10.1: Plane section of a biological structure with stereological test system superimposed. Lung of Grant's gazelle; white space is airway, dark blobs are red blood cells. Microtome thin section, optical microscope image field, magnification x 1500. Standard test system on transparency, randomly translated over photographic print. Reprinted, by permission, from Cruz- Orive and Weibel (1981~. Copyright (I) 1981 by Royal Microscopial Society.

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q.~ PLATE 10.2: A disector sample formed by two optical section planes. Hu- man renal glomerulus; dark blobs are nuclei. At left is the look-up section; at right the counting section, with a tessellation of rectangular counting frames superimposed (randomly translated). Arrows indicate nuclei counted by the disector/tiling rule. Optical microscope, Hematoxylin-Giemsa stain, mag- nification x1140, section separation 4 Am. By kind permission of Dr. Niels Marcussen, University of Aarhus, Denmark.