Image Formation by Lenses

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 Lenses Image Formation by Lenses Bởi: OpenStaxCollege Lenses are found in a huge array of optical instruments, ranging from a simple magnifying glass to the eye to a camera’s zoom lens In this section, we will use the law of refraction to explore the properties of lenses and how they form images The word lens derives from the Latin word for a lentil bean, the shape of which is similar to the convex lens in [link] The convex lens shown has been shaped so that all light rays that enter it parallel to its axis cross one another at a single point on the opposite side of the lens (The axis is defined to be a line normal to the lens at its center, as shown in [link].) Such a lens is called a converging (or convex) lens for the converging effect it has on light rays An expanded view of the path of one ray through the lens is shown, to illustrate how the ray changes direction both as it enters and as it leaves the lens Since the index of refraction of the lens is greater than that of air, the ray moves towards the perpendicular as it enters and away from the perpendicular as it leaves (This is in accordance with the law of refraction.) Due to the lens’s shape, light is thus bent toward the axis at both surfaces The point at which the rays cross is defined to be the focal point F of the lens The distance from the center of the lens to its focal point is defined to be the focal lengthf of the lens [link] shows how a converging lens, such as that in a magnifying glass, can converge the nearly parallel light rays from the sun to a small spot Rays of light entering a converging lens parallel to its axis converge at its focal point F (Ray lies on the axis of the lens.) The distance from the center of the lens to the focal point is the lens’s focal length f An expanded view of the path taken by ray shows the perpendiculars and the angles of incidence and refraction at both surfaces Converging or Convex Lens 1/22 Image Formation by Lenses The lens in which light rays that enter it parallel to its axis cross one another at a single point on the opposite side with a converging effect is called converging lens Focal Point F The point at which the light rays cross is called the focal point F of the lens Focal Length f The distance from the center of the lens to its focal point is called focal length f Sunlight focused by a converging magnifying glass can burn paper Light rays from the sun are nearly parallel and cross at the focal point of the lens The more powerful the lens, the closer to the lens the rays will cross The greater effect a lens has on light rays, the more powerful it is said to be For example, a powerful converging lens will focus parallel light rays closer to itself and will have a smaller focal length than a weak lens The light will also focus into a smaller and more intense spot for a more powerful lens The power P of a lens is defined to be the inverse of its focal length In equation form, this is P = f Power P The power P of a lens is defined to be the inverse of its focal length In equation form, this is P = f where f is the focal length of the lens, which must be given in meters (and not cm or mm) The power of a lens P has the unit diopters (D), provided that the focal length is 2/22 Image Formation by Lenses given in meters That is, D = / m, or m − (Note that this power (optical power, actually) is not the same as power in watts defined in Work, Energy, and Energy Resources It is a concept related to the effect of optical devices on light.) Optometrists prescribe common spectacles and contact lenses in units of diopters What is the Power of a Common Magnifying Glass? Suppose you take a magnifying glass out on a sunny day and you find that it concentrates sunlight to a small spot 8.00 cm away from the lens What are the focal length and power of the lens? Strategy The situation here is the same as those shown in [link] and [link] The Sun is so far away that the Sun’s rays are nearly parallel when they reach Earth The magnifying glass is a convex (or converging) lens, focusing the nearly parallel rays of sunlight Thus the focal length of the lens is the distance from the lens to the spot, and its power is the inverse of this distance (in m) Solution The focal length of the lens is the distance from the center of the lens to the spot, given to be 8.00 cm Thus, f = 8.00 cm To find the power of the lens, we must first convert the focal length to meters; then, we substitute this value into the equation for power This gives P= f = 0.0800 m = 12.5 D Discussion This is a relatively powerful lens The power of a lens in diopters should not be confused with the familiar concept of power in watts It is an unfortunate fact that the word “power” is used for two completely different concepts If you examine a prescription for eyeglasses, you will note lens powers given in diopters If you examine the label on a motor, you will note energy consumption rate given as a power in watts [link] shows a concave ...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 ... a real image is projected onto the retina by the lens of an eye Note that the image is there whether it is projected onto a screen or not Real Image 8/22 Image Formation by Lenses The image in... virtual image This is a case image Virtual Image 13/22 Image Formation by Lenses An image that is on the same side of the lens as the object and cannot be projected on a screen is called a virtual image. .. This is a case image Note that the image is in focus but the face is not, because the image is much closer to the camera taking this photograph than the face 12/22 Image Formation by Lenses (credit: