Image Formation by Mirrors

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373CHAPTER23Image Formation & DisplayImages are a description of how a parameter varies over a surface. For example, standard visualimages result from light intensity variations across a two-dimensional plane. However, light isnot the only parameter used in scientific imaging. For example, an image can be formed of thetemperature of an integrated circuit, blood velocity in a patient's artery, x-ray emission from adistant galaxy, ground motion during an earthquake, etc. These exotic images are usuallyconverted into conventional pictures (i.e., light images), so that they can be evaluated by thehuman eye. This first chapter on image processing describes how digital images are formed andpresented to human observers. Digital Image StructureFigure 23-1 illustrates the structure of a digital image. This example image isof the planet Venus, acquired by microwave radar from an orbiting spaceprobe. Microwave imaging is necessary because the dense atmosphere blocksvisible light, making standard photography impossible. The image shown isrepresented by 40,000 samples arranged in a two-dimensional array of 200columns by 200 rows. Just as with one-dimensional signals, these rows andcolumns can be numbered 0 through 199, or 1 through 200. In imaging jargon,each sample is called a pixel, a contraction of the phrase: picture element.Each pixel in this example is a single number between 0 and 255. When theimage was acquired, this number related to the amount of microwave energybeing reflected from the corresponding location on the planet's surface. Todisplay this as a visual image, the value of each pixel is converted into agrayscale, where 0 is black, 255 is white, and the intermediate values areshades of gray. Images have their information encoded in the spatial domain, the imageequivalent of the time domain. In other words, features in images arerepresented by edges, not sinusoids. This means that the spacing andnumber of pixels are determined by how small of features need to be seen, The Scientist and Engineer's Guide to Digital Signal Processing374rather than by the formal constraints of the sampling theorem. Aliasing canoccur in images, but it is generally thought of as a nuisance rather than a majorproblem. For instance, pinstriped suits look terrible on television because therepetitive pattern is greater than the Nyquist frequency. The aliasedfrequencies appear as light and dark bands that move across the clothing as theperson changes position. A "typical" digital image is composed of about 500 rows by 500 columns. Thisis the image quality encountered in television, personal computer applications,and general scientific research. Images with fewer pixels, say 250 by 250, areregarded as having unusually poor resolution. This is frequently the case withnew imaging modalities; as the technology matures, more pixels are added.These low resolution images look noticeably unnatural, and the individualpixels can often be seen. On the other end, images with more than 1000 by1000 pixels are considered exceptionally good. This is the quality of the bestcomputer graphics, high-definition television, and 35 mm motion pictures.There are also applications needing even higher resolution, requiring severalthousand pixels per side: digitized x-ray images, space photographs, and glossyadvertisements in magazines.The strongest motivation for using lower resolution images is that there arefewer pixels to handle. This is not trivial; one of the most difficult problemsin image processing is managing massive amounts of data. For example, onesecond of digital audio requires about eight kilobytes. In comparison, onesecond of television requires about eight Megabytes. Transmitting a 500 by500 pixel Image Formation by Mirrors Image Formation by Mirrors Bởi: OpenStaxCollege We only have to look as far as the nearest bathroom to find an example of an image formed by a mirror Images in flat mirrors are the same size as the object and are located behind the mirror Like lenses, mirrors can form a variety of images For example, dental mirrors may produce a magnified image, just as makeup mirrors Security mirrors in shops, on the other hand, form images that are smaller than the object We will use the law of reflection to understand how mirrors form images, and we will find that mirror images are analogous to those formed by lenses [link] helps illustrate how a flat mirror forms an image Two rays are shown emerging from the same point, striking the mirror, and being reflected into the observer’s eye The rays can diverge slightly, and both still get into the eye If the rays are extrapolated backward, they seem to originate from a common point behind the mirror, locating the image (The paths of the reflected rays into the eye are the same as if they had come directly from that point behind the mirror.) Using the law of reflection—the angle of reflection equals the angle of incidence—we can see that the image and object are the same distance from the mirror This is a virtual image, since it cannot be projected—the rays only appear to originate from a common point behind the mirror Obviously, if you walk behind the mirror, you cannot see the image, since the rays not go there But in front of the mirror, the rays behave exactly as if they had come from behind the mirror, so that is where the image is situated 1/14 Image Formation by Mirrors Two sets of rays from common points on an object are reflected by a flat mirror into the eye of an observer The reflected rays seem to originate from behind the mirror, locating the virtual image Now let us consider the focal length of a mirror—for example, the concave spherical mirrors in [link] Rays of light that strike the surface follow the law of reflection For a mirror that is large compared with its radius of curvature, as in [link](a), we see that the reflected rays not cross at the same point, and the mirror does not have a welldefined focal point If the mirror had the shape of a parabola, the rays would all cross at a single point, and the mirror would have a well-defined focal point But parabolic mirrors are much more expensive to make than spherical mirrors The solution is to use a mirror that is small compared with its radius of curvature, as shown in [link](b) (This is the mirror equivalent of the thin lens approximation.) To a very good approximation, this mirror has a well-defined focal point at F that is the focal distance f from the center of the mirror The focal length f of a concave mirror is positive, since it is a converging mirror (a) Parallel rays reflected from a large spherical mirror not all cross at a common point (b) If a spherical mirror is small compared with its radius of curvature, parallel rays are focused to a common point The distance of the focal point from the center of the mirror is its focal length f Since this mirror is converging, it has a positive focal length Just as for lenses, the shorter the focal length, the more powerful the mirror; thus, P = / f for a mirror, too A more strongly curved mirror has a shorter focal length and a greater power Using the law of reflection and some simple trigonometry, it can be shown that the focal length is half the radius of curvature, or R f = 2, where R is the radius of curvature of a spherical mirror The smaller the radius of curvature, the smaller the focal length and, thus, the more powerful the mirror The convex mirror shown in [link] also has a focal point Parallel rays of light reflected from the mirror seem to originate from the point F at the focal distance f behind 2/14 Image Formation by Mirrors the mirror The focal length and power of a convex mirror are negative, since it is a diverging mirror Parallel rays of light reflected from a convex spherical mirror (small in size compared with its radius of curvature) seem to originate from a well-defined focal point at the focal distance f behind the mirror Convex mirrors diverge light rays and, thus, have a negative focal length Ray tracing is as useful for mirrors as for lenses The rules for ray tracing for mirrors are based on the illustrations just discussed: A ray approaching a concave converging mirror parallel to its axis is reflected through the focal point F of the mirror on the same side (See rays and in [link](b).) A ray approaching a convex diverging mirror parallel to its axis is reflected so that it seems to come from the focal point F behind the mirror (See rays and in [link].) Any ray striking the center of a mirror is followed by applying the law of reflection; it makes the same angle with the axis when leaving as when approaching (See ray in [link].) A ray approaching a concave converging mirror through its focal point is ...REVIEW ARTICLE Membrane targeting and pore formation by the type III secretion system translocon Pierre-Jean Matteı ¨ 1 , Eric Faudry 2 , Viviana Job 1 , Thierry Izore ´ 1 , Ina Attree 2 and Andre ´ a Dessen 1 1 Bacterial Pathogenesis Group, Institut de Biologie Structurale, UMR 5075 (CNRS ⁄ CEA ⁄ UJF), Grenoble, France 2 Bacterial Pathogenesis and Cellular Responses Team, Centre National de la Recherche Scientifique (CNRS), Universite ´ Joseph Fourier (UJF), LBBSI, iRTSV, CEA, Grenoble, France Introduction Type III secretion systems (T3SS) are complex macro- molecular machineries employed by a number of bac- teria to inject toxins and effectors directly into the cytoplasm of eukaryotic cells. Pathogens carrying this system, which include Pseudomonas, Yersinia, Salmo- nella and Shigella spp., as well as clinical Escherichia coli isolates, can translocate between four and 20 effec- tors with dramatic effects on the target cell, leading, for example, to cytoskeleton rearrangement, membrane disruption or the initiation of apoptosis [1–3]. T3SS are composed of at least twenty distinct pro- teins that assemble into three major parts. The basal body of the system, composed of two main ring-like structures, spans both the inner and outer bacterial membranes (Fig. 1) [4–7]. This multi-protein structure is associated with an ATPase, which itself is mem- brane-associated and faces the bacterial cytoplasm, and is suggested to be involved in facilitating the entry of export substrates into the secretion system [8–10]. The basal body of the T3SS is also associated with a proteinaceous needle that extends outwards from the bacterial surface and is assumed to act as a conduit for effector secretion [6,11–13], although direct evi- dence for this concept is lacking. Because the internal diameter of the needle is relatively small (2.0–2.5 nm), effectors probably travel in unfolded ⁄ semi-unfolded states [11]. Synthesis and assembly of the T3SS itself are induced once the bacterium is physically associated Keywords bacterial infection; injection; membrane; pore formation; secretion; toxin Correspondence A. Dessen, Bacterial Pathogenesis Group, Institut de Biologie Structurale, UMR 5075 (CNRS ⁄ CEA ⁄ UJF), 41 rue Jules Horowitz, 38027 Grenoble, France Fax: +33 4 38 78 54 94 Tel: +33 4 38 78 95 90 E-mail: andrea.dessen@ibs.fr (Received 21 September 2010, revised 4 November 2010, accepted 26 November 2010) doi:10.1111/j.1742-4658.2010.07974.x The type III secretion system (T3SS) is a complex macromolecular machin- ery employed by a number of Gram-negative species to initiate infection. Toxins secreted through the system are synthesized in the bacterial cyto- plasm and utilize the T3SS to pass through both bacterial membranes and the periplasm, thus being introduced directly into the eukaryotic cytoplasm. A key element of the T3SS of all bacterial pathogens is the translocon, which comprises a pore that is inserted into the membrane of the target cell, allowing toxin injection. Three macromolecular partners associate to form the translocon: two are hydrophobic and one is hydrophilic, and the latter also associates with the T3SS needle. In this review, we discuss recent advances on the biochemical and structural characterization of the proteins involved in translocon formation, as well as their participation in the modi- fication of intracellular signalling pathways upon infection. Models of tran- slocon assembly and regulation are also discussed. Abbreviations EHEC, enterohaemorrhagic; EPEC, enteropathogenic; IFN, interferon; Proceedings of the COLING/ACL 2006 Main Conference Poster Sessions, pages 547–554, Sydney, July 2006. c 2006 Association for Computational Linguistics Discriminating image senses by clustering with multimodal features Nicolas Loeff Dept. of Computer Science University of Illinois, UC loeff@uiuc.edu Cecilia Ovesdotter Alm Dept. of Linguistics University of Illinois, UC ebbaalm@uiuc.edu David A. Forsyth Dept. of Computer Science University of Illinois, UC daf@uiuc.edu Abstract We discuss Image Sense Discrimination (ISD), and apply a method based on spec- tral clustering, using multimodal features from the image and text of the embedding web page. We evaluate our method on a new data set of annotated web images, re- trieved with ambiguous query terms. Ex- periments investigate different levels of sense granularity, as well as the impact of text and image features, and global versus local text features. 1 Introduction and problem clarification Semantics extends beyond words. We focus on im- age sense discrimination (ISD) 1 for web images retrieved from ambiguous keywords, given a mul- timodal feature set, including text from the doc- ument which the image was embedded in. For instance, a search for CRANE retrieves images of crane machines, crane birds, associated other ma- chinery or animals etc., people, as well as images of irrelevant meanings. Current displays for im- age queries (e.g. Google or Yahoo!) simply list retrieved images in any order. An application is a user display where images are presented in se- mantically sensible clusters for improved image browsing. Another usage of the presented model is automatic creation of sense discriminated image data sets, and determining available image senses automatically. ISD differs from word sense discrimination and disambiguation (WSD) by increased complexity in several respects. As an initial complication, both word and iconographic sense distinctions 1 Cf. (Sch ¨ utze, 1998) for a definition of sense discrimina- tion in NLP. matter. Whereas a search term like CRANE can refer to, e.g. a MACHINE or a BIRD; iconographic distinctions could additionally include birds stand- ing, vs. in a marsh land, or flying, i.e. sense- distinctions encoded by further descriptive modi- fication in text. Therefore, as the number of text senses grow with corpus size, the iconographic senses grow even faster, and enumerating icono- graphic senses is extremely challenging; espe- cially since dictionary senses do not capture icono- graphic distinctions. Thus, we focus on image- driven word senses for ISD, but we acknowledge the importance of iconography for visual meaning. Also, an image often depicts a related mean- ing. E.g. a picture retrieved for SQUASH may depict a squash bug (i.e. an insect on a leaf of a squash plant) instead of a squash vegetable, whereas this does not really apply in WSD, where each instance concerns the ambiguous term itself. Therefore, it makes sense to consider the divi- sion between core sense, related sense, and un- related sense in ISD, and, as an additional com- plication, their boundaries are often blurred. Most importantly, whereas the one-sense-per-discourse assumption (Yarowsky, 1995) also applies to dis- criminating images, there is no guarantee of a local collocational or co-occurrence context around the target image. Design or aesthetics may instead determine image placement. Thus, con- sidering local text around the image may not be as helpful as local context is for standard IMAGE ESTIMATION BY EXAMPLE: Geophysical soundings image construction Multidimensional autoregression Jon F. Claerbout Cecil and Ida Green Professor of Geophysics Stanford University with Sergey Fomel Stanford University c  February 28, 2006 dedicated to the memory of Johannes “Jos” Claerbout 1974-1999 “What do we have to look forward to today? There are a lot of things we have to look forward to today.” http://sep.stanford.edu/sep/jon/family/jos/ Contents 1 Basic operators and adjoints 1 1.1 FAMILIAR OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 ADJOINT DEFINED: DOT-PRODUCT TEST . . . . . . . . . . . . . . . . 27 2 Model fitting by least squares 33 2.1 HOW TO DIVIDE NOISY SIGNALS . . . . . . . . . . . . . . . . . . . . . 33 2.2 MULTIVARIATE LEAST SQUARES . . . . . . . . . . . . . . . . . . . . . 39 2.3 KRYLOV SUBSPACE ITERATIVE METHODS . . . . . . . . . . . . . . . 45 2.4 INVERSE NMO STACK . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.5 VESUVIUS PHASE UNWRAPPING . . . . . . . . . . . . . . . . . . . . . 57 2.6 THE WORLD OF CONJUGATE GRADIENTS . . . . . . . . . . . . . . . . 66 2.7 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3 Empty bins and inverse interpolation 73 3.1 MISSING DATA IN ONE DIMENSION . . . . . . . . . . . . . . . . . . . . 74 3.2 WELLS NOT MATCHING THE SEISMIC MAP . . . . . . . . . . . . . . . 82 3.3 SEARCHING THE SEA OF GALILEE . . . . . . . . . . . . . . . . . . . . 87 3.4 INVERSE LINEAR INTERPOLATION . . . . . . . . . . . . . . . . . . . . 90 3.5 PREJUDICE, BULLHEADEDNESS, AND CROSS VALIDATION . . . . . 94 4 The helical coordinate 97 4.1 FILTERING ON A HELIX . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.2 FINITE DIFFERENCES ON A HELIX . . . . . . . . . . . . . . . . . . . . 107 CONTENTS 4.3 CAUSALITY AND SPECTAL FACTORIZATION . . . . . . . . . . . . . . 111 4.4 WILSON-BURG SPECTRAL FACTORIZATION . . . . . . . . . . . . . . 116 4.5 HELIX LOW-CUT FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.6 THE MULTIDIMENSIONAL HELIX . . . . . . . . . . . . . . . . . . . . . 123 4.7 SUBSCRIPTING A MULTIDIMENSIONAL HELIX . . . . . . . . . . . . . 124 5 Preconditioning 131 5.1 PRECONDITIONED DATA FITTING . . . . . . . . . . . . . . . . . . . . . 131 5.2 PRECONDITIONING THE REGULARIZATION . . . . . . . . . . . . . . 132 5.3 OPPORTUNITIES FOR SMART DIRECTIONS . . . . . . . . . . . . . . . 137 5.4 NULL SPACE AND INTERVAL VELOCITY . . . . . . . . . . . . . . . . . 138 5.5 INVERSE LINEAR INTERPOLATION . . . . . . . . . . . . . . . . . . . . 143 5.6 EMPTY BINS AND PRECONDITIONING . . . . . . . . . . . . . . . . . . 146 5.7 THEORY OF UNDERDETERMINED LEAST-SQUARES . . . . . . . . . . 150 5.8 SCALING THE ADJOINT . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.9 A FORMAL DEFINITION FOR ADJOINTS . . . . . . . . . . . . . . . . . 153 6 Multidimensional autoregression 155 6.1 SOURCE WAVEFORM, MULTIPLE REFLECTIONS . . . . . . . . . . . . 156 6.2 TIME-SERIES AUTOREGRESSION . . . . . . . . . . . . . . . . . . . . . 157 6.3 PREDICTION-ERROR FILTER OUTPUT IS WHITE . . . . . . . . . . . . 159 6.4 PEF ESTIMATION WITH MISSING DATA . . . . . . . . . . . . . . . . . 174 6.5 TWO-STAGE LINEAR LEAST SQUARES . . . . . . . . . . . . . . . . . . 178 6.6 BOTH MISSING DATA AND UNKNOWN FILTER . . . . . . . . . . . . . 186 6.7 LEVELED INVERSE INTERPOLATION . . . . . . . . . . . . . . . . . . . 190 6.8 MULTIVARIATE SPECTRUM . . . . . . . . . . . . . . . . . . . . . . . . 194 7 Noisy data 199 7.1 MEANS, MEDIANS, PERCENTILES AND MODES . . . . . . . . . . . . 199 7.2 NOISE BURSTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 7.3 MEDIAN BINNING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 CONTENTS 7.4 ROW NORMALIZED PEF . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 7.5 DEBURST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multilayer TiO 2 –Nanotube Formation by Two-Step Anodization J. M. Macak, * S. Albu, D. H. Kim, I. Paramasivam, S. Aldabergerova, and P. Schmuki ** ,z Department of Materials Science, University of Erlangen–Nuremberg, D-91058 Erlangen, Germany In this work we report on the growth of a closely stacked double layer of a self-organized TiO 2 nanotubes. For that we first anodize Ti in acidic electrolyte containing hydrofluoric acid to form thin nanotube layers. Afterwards we start a second anodization in a different electrolyte, a glycerol/NH 4 F mixture. This procedure allows us to grow the second layer directly underneath the first one. From scanning electron microscopy and transmission electron microscopy investigations we revealed that the second growth occurs via the tube bottoms of the first layer. These stacked multilayers generate new possibilities to vertically tailor the properties of the self-organized TiO 2 nanotube layers. © 2007 The Electrochemical Society. ͓DOI: 10.1149/1.2737544͔ All rights reserved. Manuscript submitted February 5, 2007; revised manuscript received April 8, 2007. Available electronically May 15, 2007. Formation of porous alumina based on anodic oxidation of alu- minium has been investigated and well understood already for many years. 1,2 But only about one decade ago, extremely ordered and self-organized porous alumina structures could be formed using a set of specific electrochemical conditions using optimized potential, temperature, electrolyte composition, etc. 3-7 In 1999, Zwilling et al. 8 showed that Ti can also be converted to highly ordered nanotubes ͑in contrast to alumina nanopores͒ using self-assembly during an- odic oxidation. Since then there have been many efforts to tailor the morphology of the TiO 2 nanotube toward enabling potential applications. 9-13 Later on, other valve metals have shown the ability to form nanotubes. 14-16 In all these works, fluoride-anion-containing electrolytes were used to selectively dissolve the anodized metals under anodic bias applied for several hours, leaving nanotubular layers on their surfaces. Although there is still very little work done on Ti and other metals compared to Al, reports showing significant improvements in length 9-13 and tube diameter 17,18 have been re- cently published by our group as well as by others. 19,20 Typically, the diameter of tubes is controlled by the applied anodization voltage 17 and various lengths can be obtained using different elec- trolytes. All these anodic TiO 2 nanotubes have already been used for a wide range of different applications, such as those based on the semiconductive nature of TiO 2 . 21 Namely, dye-sensitization, 22 doping, 23-25 photocatalysis, 26 electrochromism, 27 and photolysis 28 have been demonstrated, as well as others based on catalysis 29 or sensing. 30 Due to high biocompatibility of TiO 2 , other reports tar- geted growth of a hydroxyapatite layer on the nanotubes 31 as well as their formation on Ti alloys. 32,33 It has also been shown that the structure of the anodized tubes is always amorphous and can be converted by annealing to anatase 21,34,35 or, e.g., BaTiO 3 36 or Ba͑Sr͒TiO 3 37 upon hydrothermal alkali treatment. Additionally, by electrochemical deposition into the tubes, 38 properties such as the magnetic behavior of nanotube layers can be modified. 39 In the present work we show that even multistacks of TiO 2 nano- tubes can be grown directly by a two-step anodization process. Experimental Titanium foils ͑0.1 mm, 99.6% purity, Advent Materials͒ were degreased by sonication in acetone, isopropanol, and methanol prior to electrochemical experiments, afterward rinsed with deionized ͑DI͒ water, and finally dried in nitrogen stream. The samples were pressed together with a Cu plate against an O-ring in an electro- chemical cell ͑1cm 2 exposed to the electrolyte͒ and anodized ... Since the image is behind the mirror, it cannot be projected and is thus a virtual image It is also seen to be smaller than the object 8/14 Image Formation by Mirrors Case images for mirrors are... magnification The three types of images formed by mirrors (cases 1, 2, and 3) are exactly analogous to those formed by lenses, as summarized in the table at the end of Image Formation by Lenses It is easiest... case image for mirrors and is exactly analogous to that for lenses 7/14 Image Formation by Mirrors (a) Case images for mirrors are formed when a converging mirror has an object closer to it than