Pellentesque dictum placerat consequat. Nam pulvinar placerat tortor id tempor. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut vel leo et dolor hendrerit blandit. Praesent efficitur placerat est. Vivamus venenatis feugiat malesuada. Maecenas mattis, justo eget gravida dapibus, velit justo euismod velit, mollis varius neque sem ac quam. Aenean vel luctus eros, non vehicula nunc. Praesent eget bibendum lorem, eu ultricies mauris. Morbi convallis lectus nulla, id tristique nisl sollicitudin nec. Suspendisse potenti. Vivamus sit amet sem vel eros porta mollis et et nisl. Mauris rutrum nisl sed ante dapibus mattis. Cras vehicula consequat turpis, eu maximus ipsum elementum ut. Proin dui nisi, pulvinar ac volutpat porttitor, elementum nec dolor. Pellentesque sit amet mi dignissim, suscipit elit ut, mattis augue. Duis libero nisl, consectetur accumsan ipsum vel, finibus euismod diam. Vestibulum iaculis odio ac libero consequat, a ullamcorper nisi consectetur. Curabitur mattis vitae magna sed rutrum. Nulla ornare ut enim a aliquet. Nunc felis magna, pharetra at orci vitae, tincidunt pharetra leo. Morbi rhoncus leo nisi. Ut commodo magna eu nisl faucibus, imperdiet viverra nulla blandit. Suspendisse et elit a o;rci rhoncus congue ornare id arcu. Nullam ut eleifend lorem. Proin egestas dolor tellus, varius tincidunt sapien mollis sed. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin sodales massa eget sem accumsan suscipit. Cras euismod nec lacus eget vehicula. Aliquam aliquet urna eu leo pulvinar auctor. Morbi lorem augue, ultricies viverra interdum ut, ornare eu ante. Pellentesque vel odio nec nisi malesuada commodo. Sed ac orci facilisis, sollicitudin velit ut, posuere ex. Morbi at gravida risus. Proin at sapien ac eros sollicitudin egestas eget vitae metus. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Nam egestas turpis consequat pharetra rutrum. Suspendisse mi lacus, pretium eu venenatis eu, aliquam ut eros. Pellentesque gravida tincidunt nisl, ac sollicitudin orci. Duis nulla est, ornare eu volutpat ut, convallis quis nunc. Curabitur porta mi non lectus viverra porta. Praesent eu metus enim. Sed euismod, nulla nec tempus porttitor, dolor ex consequat risus, sed sodales justo magna vitae felis. Aenean eget orci laoreet neque tincidunt egestas eu vitae neque. Integer fermentum odio enim, in imperdiet neque suscipit at. Integer a odio tellus. Vestibulum sit amet ligula et metus dignissim sollicitudin. Suspendisse posuere ullamcorper vulputate. Etiam sodales eleifend nibh, nec gravida augue vulputate eu. Proin arcu felis, pulvinar cursus sapien ac, cursus gravida nisl. Phasellus tempus iaculis blandit. Quisque et dui suscipit, vulputate nulla a, hendrerit dui. Etiam a porta neque, nec rutrum erat. Maecenas feugiat orci eu mi blandit ultricies. Morbi scelerisque, augue a egestas sagittis, est dolor rutrum augue, et facilisis sapien magna at ligula. Aenean et tortor nec ex porttitor venenatis. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Nulla lacus mi, dapibus at mauris a, facilisis posuere quam. Aenean accumsan purus sed purus pharetra, eu dapibus elit venenatis. Suspendisse efficitur condimentum velit pretium volutpat. Nulla nec enim sed ex vehicula condimentum id sed leo. Donec eu rutrum urna, rhoncus faucibus lacus. Aliquam elementum dolor id ipsum consectetur egestas. The advent of sophisticated photo editing software has made it increasingly easier to manipulate digital images. Often visual inspection cannot definitively distinguish the resulting forgeries from authentic photographs. In response, forensic techniques have emerged to detect geometric or statistical inconsistencies that result from specific forms of photo manipulation. In this paper we describe a new forensic technique that focuses on geometric inconsistencies that arise when fake reflections are inserted into a photograph or when a photograph containing reflections is manipulated. This analysis employs basic rules of reflective geometry and linear perspective projection, makes minimal assumptions about the scene geometry, and only requires the user to identify corresponding points on an object and its reflection. The analysis is also insensitive to common image editing operations such as resampling, color manipulations, and lossy compression. We demonstrate this technique with both visually plausible forgeries of our own creation and commercially produced forgeries. We describe a method for detecting physical inconsistencies in lighting from the shading and shadows in an image. This method imposes a multitude of shading- and shadow-based constraints on the projected location of a distant point light source. The consistency of a collection of such constraints is posed as a linear programming problem. A feasible solution indicates that the combination of shading and shadows is physically consistent, while a failure to find a solution provides evidence of photo tampering. This paper presents a fast tight-tolerance threading technique for string and rope. Instead of relying on simulations of these deformable objects to plan a path or compute control actions, we control the movement of the string with a virtual magnetic vector field emanating from the narrow openings we wish to thread through. We compute an approximate Jacobian to move the tip of the string through the vector field and propose a method to promote alignment of the head of the string to the opening. We also propose a method for re-grasping the string based on the relationship between the strings configuration, the orientation of the opening, and direction of gravity. This re-grasping method in conjunction with our controller can be used to thread the string through a sequence of openings. We evaluated our method in simulation (with simulated sensor noise) and on the Da Vinci surgical robot. Our results suggest that our method is quite robust to errors in sensing, and is capable of real-world threading tasks with the da Vinci robot, where the diameter of the string and opening differ by only one millimeter. String stretched tightly along a sequence of fixed grasp points takes the shape of a polygonal arc. In this work, we investigate how many points are necessary and sufficient to grasp and tie arbitrary knots while maintaining tension, so that the string remains polygonal. This approach allows reasoning that is entirely geometric, which does not rely on potentially inaccurate dynamic models of the string or detailed knowledge of physical characteristics of the string. Algorithms are proposed to determine the contact locations, and generate the motions needed to tie arbitrary knots. This work shows that a number of grasp points that is linear in the number of crossings in a knot diagram is sufficient to immobilize string in a polygonal shape with the topology of an arbitrary knot, or to fold or unfold the knot from a straight configuration. Praesent molestie ipsum eu magna rhoncus gravida. Sed interdum felis vitae orci pretium, tincidunt varius nibh varius. Aenean imperdiet egestas condimentum. Quisque volutpat molestie ullamcorper. Mauris faucibus molestie elit id posuere. Donec tortor erat, luctus ut neque a, porttitor convallis turpis. Nam mollis quam nec arcu fermentum tristique. Etiam tempor augue ante, eu dictum lacus tincidunt vel. Etiam mi dolor, mollis at egestas id, sodales at ex. Nulla hendrerit nibh sapien, sed tempus purus mattis eu. Nulla velit ligula, feugiat sed congue et, placerat ac augue. Sed risus leo, eleifend a dolor nec, porta imperdiet purus. Aenean tincidunt justo at scelerisque pharetra. Ut lacinia mi et fermentum condimentum. Nam lacus lacus, aliquam vitae magna eget, ornare facilisis erat. Quisque ut metus et dolor blandit dictum sit amet ac nisi. Aliquam pellentesque, libero sed feugiat maximus, ante turpis commodo nulla, eu interdum odio ante vitae tellus. Fusce in nisl odio. Ut ut diam augue. In ligula nunc, congue non hendrerit molestie, euismod ac risus. When creating a photographic composite, it can be difficult to match lighting conditions. We describe a technique for measuring lighting conditions in an image, and describe its use in detecting photographic composites. Specifically, we describe how to approximate a three-dimensional lighting environment with a low-dimensional model and how to estimate the models parameters from a single image. Inconsistencies in the lighting model are then used as evidence of tampering. Nam blandit nec ante id pellentesque. Aenean orci felis, ultricies aliquam pellentesque sed, rutrum sit amet eros. Ut gravida leo tellus, ac ultrices augue aliquet nec. Integer hendrerit pulvinar turpis non pellentesque. Curabitur ac est viverra, egestas felis sed, porttitor nunc. Aliquam condimentum lacinia purus, nec volutpat ex faucibus quis. Nam faucibus placerat metus, quis imperdiet sem gravida sit amet. Nam pellentesque nulla id massa malesuada, id ultrices urna eleifend. Mauris interdum, metus porta imperdiet finibus, urna elit egestas libero, ut tincidunt nulla turpis eu elit. Morbi auctor accumsan lobortis. Donec molestie vulputate enim et molestie. Donec aliquam turpis vitae sapien pretium, at sollicitudin magna convallis. Aliquam at molestie nisl. Aenean venenatis elit in nisi efficitur convallis. Duis augue libero, ullamcorper bibendum diam quis, ultrices sollicitudin enim. In sed libero sit amet mauris blandit scelerisque a iaculis diam. Maecenas malesuada ante augue. Morbi malesuada sem finibus eros malesuada, et aliquet justo auctor. Proin ipsum magna, bibendum at placerat nec, semper non eros. Nam mauris magna, scelerisque quis leo nec, venenatis ultricies augue. Fusce lobortis efficitur mauris. Sed purus ipsum, tincidunt vel lectus vitae, aliquam tristique risus. Nullam vel eros nec nisi ultrices molestie. Nulla facilisi. This paper introduces a fast weighted streaming spanner algorithm (WSS) that trims edges from roadmaps generated by robot motion planning algorithms such as Probabilistic Roadmap (PRM) and variants (e.g. k-PRM) as the edges are generated, but before collision detection; no route in the resulting graph is more than a constant factor larger than it would have been in the original roadmap. Experiments applying WSS to k-PRM were conducted, and the results shows our algorithms capability to filter graphs with up to one million vertices, discarding about three-quarters of the edges. Due to the fact that many collision detection steps can be avoided, the combination of WSS and k-PRM is faster than k-PRM alone. The paper further presents an online directed spanner algorithm that can be used for systems with non-holonomic constraints, with proof of correctness and experimental results. This paper presents a controlled tying approach for knots using fixtures and simple pulling motions applied to the ends of string. Each fixture is specific to a particular knot; the paper gives a design process that allows a suitable fixture to be designed for an input knot. Knot tying is separated into two phases. In the first phase, a fixture is used to loosely arrange the string around a set of rods, with the required topology of the given knot. In the second phase, the string is pulled taut around the tightening fixtures. Two sets of tightening fixture designs are presented. The first design is a fixture with no moving parts; tilted rods whose cross-sections get closer near the tips, guiding string in a controlled fashion as string slides up the rods during tightening. The second design is a collection of straight rods that can move passively along predefined paths during tightening. Successful tying is shown for three interesting cases: a cloverleaf knot design, a double coin knot design, and the top of a shoelace knot. The manipulation of text on a sign or billboard is relatively easy to do in a way that is perceptually convincing. When text is on a planar surface and imaged under perspective projection, the text undergoes a specific distortion. When text is manipulated, it is unlikely to precisely satisfy this geometric mapping. We describe a technique for detecting if text in an image obeys the expected perspective projection, deviations from which are used as evidence of tampering. We describe a new concept for making photo tampering more difficult and time consuming, and for a given amount of time and effort, more amenable to detection. We record the camera preview and camera motion in the moments just prior to image capture. This information is packaged along with the full resolution image. To avoid detection, any subsequent manipulation of the image would have to be propagated to be consistent with this data, a decidedly difficult undertaking. Aliquam placerat auctor posuere. Pellentesque maximus tristique elit. Mauris nec fringilla massa. Praesent risus enim, consectetur non efficitur sed, luctus eget nunc. Sed eget finibus purus, ac tincidunt magna. Sed vel neque egestas, hendrerit elit ac, dictum eros. Nullam elementum congue orci, at euismod leo ultrices et. Aenean malesuada volutpat elit ut iaculis. Donec ac diam velit. Nunc posuere rhoncus sem, a maximus ex condimentum ac. Aenean ut augue in dolor facilisis efficitur sit amet a odio. Nam sodales nisl id laoreet congue. Orci varius natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Phasellus nec urna ut purus consequat pulvinar. Suspendisse orci mauris, euismod sit amet ligula et, faucibus convallis lacus. Cras a nisl id sapien imperdiet elementum. Maecenas vel viverra nunc. Quisque ultricies ac libero in pharetra. Ut id tortor felis. Vestibulum facilisis tincidunt orci, ac lacinia orci scelerisque et. Vestibulum suscipit, velit eget ullamcorper finibus, lacus augue egestas metus, at laoreet sapien turpis quis tellus. Suspendisse sodales commodo ante in fringilla. Maecenas blandit pretium iaculis. Aenean dapibus nunc leo, sit amet interdum lectus hendrerit at. Aliquam quis rhoncus risus. Maecenas in nisl aliquam, iaculis ex vel, scelerisque nisi. Proin efficitur rhoncus tellus id sollicitudin. Fusce quis nunc pretium, volutpat felis ut, dictum lectus. Suspendisse dictum mi eget arcu volutpat tristique. Proin aliquet ante in mi rutrum, sit amet tincidunt ante cursus. Morbi sodales justo ut elit sodales interdum. Proin lobortis condimentum libero, dapibus dignissim libero lacinia eget. Sed lobortis tortor vel pulvinar tincidunt. Vestibulum sem augue, fermentum nec tellus gravida, posuere molestie arcu. Morbi sit amet felis et risus tempus feugiat. Fusce porttitor mollis consectetur. Curabitur nec turpis lacus. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Aliquam sodales massa a elit aliquam, ut gravida arcu varius. Mauris sed quam justo. Cras id felis a ligula placerat lobortis. Nam massa leo, malesuada et maximus eu, mattis non ligula. Nullam tempor metus tortor, vitae faucibus magna imperdiet tincidunt. Donec tristique massa a libero fermentum venenatis. Donec lacinia tincidunt tortor. Aliquam fermentum lectus felis, sit amet sollicitudin leo iaculis nec. Quisque sollicitudin ullamcorper ligula quis commodo. Aenean sollicitudin malesuada sapien ac vestibulum. Etiam dapibus imperdiet diam, et imperdiet felis laoreet non. Nam ac magna condimentum, placerat nisi sed, malesuada urna. Phasellus aliquam nisi vel orci sodales, sed elementum dui malesuada. Fusce blandit ornare malesuada. Phasellus non nisi lacus. Aenean in nisi quis turpis posuere facilisis. Duis pharetra placerat velit et consequat. Proin vitae nulla enim. Praesent tellus leo, consequat at pharetra accumsan, volutpat eu velit. Vestibulum in dapibus dui, condimentum volutpat lacus. Aenean a malesuada tortor. Duis lectus mauris, imperdiet eu volutpat vel, condimentum pharetra dui. Vestibulum massa leo, porttitor at lacinia aliquet, sagittis ut ligula. Vestibulum bibendum id ipsum et lobortis. Aliquam eget lorem pulvinar, malesuada lectus ut, mollis erat. Suspendisse tempus eu enim a convallis. Donec vitae nisl nec ante condimentum pretium in a purus. Nulla condimentum faucibus lacus, nec tempor elit bibendum quis. Cras elit elit, tempor vitae semper id, mattis id elit. Aliquam non augue lacus. Praesent interdum tortor ac imperdiet consectetur. Mauris felis nunc, tristique ut suscipit nec, semper ac magna. Fusce accumsan ultrices erat, vitae volutpat felis interdum vitae. Suspendisse malesuada id lorem a vulputate. Interdum et malesuada fames ac ante ipsum primis in faucibus. In eu ullamcorper massa, vitae posuere augue. In orci neque, ullamcorper quis ultricies quis, condimentum quis lacus. Phasellus sit amet metus id est sollicitudin tincidunt. Duis vitae posuere libero. Vestibulum vestibulum mi ut arcu facilisis tincidunt et eget massa. Aenean ornare ipsum quis ipsum commodo, vitae euismod dolor fermentum. Etiam maximus mi eget condimentum venenatis. Nulla eget eros vel justo pellentesque congue et a ligula. Suspendisse posuere tempor turpis vel molestie. Donec id nisl egestas, interdum neque et, vestibulum tellus. Fusce at lacinia turpis. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; The optimal trajectory with respect to some metric may require very many switches between controls, or even infinitely many, a phenomenon called chattering; this can be problematic for existing motion planning algorithms that plan using a finite set of motion primitives. One remedy is to add some penalty for switching between controls. This paper explores the implications of this switching cost for optimal trajectories, using rigid bodies in the plane (which have been studied extensively in the cost-free-switch model) as an example system. Blatts Indifference Principle (BIP) is used to derive necessary conditions on optimal trajectories; Lipschitzian optimization techniques together with an A-star search yield an algorithm for finding trajectories that can arbitrarily approximate the optimal trajectories. This paper presents a definition of convexity useful for describing local optimality in configuration spaces, proves that finding convex regions is relatively easy, and presents an algorithm for approximating the free configuration space using a set of such convex regions. The paper examines simple but interesting systems: serial planar arms with revolute joints, and a Reeds-Shepp car. The paper experimentally explores an approach for finding good (although not necessarily optimal) trajectories using the derived data structure. Fifty years have passed since the assassination of U.S. President Kennedy. Despite the long passage of time, it is still argued that the famous backyard photo of Oswald, holding the same type of rifle used to assassinate the President, is a fake. These claims include, among others, that Oswalds pose in the photo is physically implausible. We describe a detailed three-dimensional stability analysis to determine if this claim is warranted Integer suscipit commodo sollicitudin. Mauris vitae aliquam augue. Aliquam pretium sagittis ante, et convallis diam tempus sit amet. Ut vulputate sem at rutrum varius. Morbi vel nulla commodo, consectetur nulla ut, lobortis mauris. Duis ornare mauris ac leo luctus ultrices. Interdum et malesuada fames ac ante ipsum primis in faucibus. Aenean semper, risus quis vestibulum ullamcorper, nisl quam viverra risus, at aliquam est tellus ut justo. Ut sed rutrum ex. Pellentesque et nibh sit amet erat dapibus semper. Nunc quis diam pulvinar, hendrerit purus ut, interdum libero. Vestibulum at convallis diam. Vestibulum nunc quam, vestibulum eu augue ut, cursus commodo turpis. Aliquam mollis id est in rhoncus. Sed aliquet odio a molestie tincidunt. Morbi quis velit sapien. Orci varius natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Morbi eu aliquam quam. Nam et arcu risus. Fusce sodales tempus neque quis venenatis. Etiam ipsum felis, lobortis et turpis eget, maximus dictum est. Curabitur sagittis sollicitudin nibh eu pulvinar. Suspendisse nibh orci, luctus a odio sit amet, iaculis vestibulum elit. Cras mattis pellentesque orci id tincidunt. Cras congue erat dolor, eu laoreet urna imperdiet vitae. Aliquam erat volutpat. We describe a photo forensic technique based on detecting inconsistencies in lighting. This technique explicitly measures the three-dimensional lighting properties for individual people, objects, or surfaces in a single image. We show that with minimal training, an analyst can accurately specify three-dimensional shape in a single image from which three-dimensional lighting can be automatically estimated. A perturbation analysis on the estimated lighting is performed to yield a probabilistic measure of the location of the illuminating light. Inconsistencies in lighting within an image evidence photo tampering. We describe a geometric technique to detect physically inconsistent arrangements of shadows in an image. This technique combines multiple constraints from cast and attached shadows to constrain the projected location of a point light source. The consistency of the shadows is posed as a linear programming problem. A feasible solution indicates that the collection of shadows is physically plausible, while a failure to find a solution provides evidence of photo tampering. We present a class of fixtures that can be disassembled into four pieces to extract the loosely-tied knot. We prove that a fixture can be designed for any particular knot such that the knot can be extracted using only simple pure translations of the four fixture sections. We explore some of the issues raised by our experimental work with these fixtures, which show that simple knots can be tied extremely quickly (less than half a second) and reliably using four-piece fixtures. Nulla sapien neque, pulvinar vel imperdiet sit amet, luctus at felis. Etiam tempor vel ipsum quis eleifend. Praesent et massa ornare, consectetur neque at, porttitor quam. Mauris condimentum arcu vitae arcu fermentum, a pharetra velit fringilla. Suspendisse quis hendrerit nisi. Proin rhoncus ex nec enim sollicitudin, et iaculis ligula ullamcorper. Cras fermentum bibendum blandit. Cras pellentesque tristique augue et imperdiet. Praesent vestibulum mauris eget purus volutpat, sit amet convallis orci eleifend. Aenean pharetra quis nulla consequat tincidunt. Phasellus in sapien ipsum. Ut porta ex a blandit tempor. Aenean ac eleifend leo. Orci varius natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Aliquam egestas blandit ex sed vehicula. Donec tempus tempus diam, non sollicitudin ligula pretium eget. Vivamus lobortis volutpat nibh, vel condimentum justo consequat id. Pellentesque dapibus ex elit, in gravida tellus egestas vel. Sed feugiat molestie justo iaculis ullamcorper. Ut mollis eros quis ipsum iaculis imperdiet. Maecenas bibendum arcu ac dolor sagittis, cursus faucibus metus imperdiet. The optimal trajectory with respect to some metric for a system with a discrete set of controls may require very many switches between controls, or even infinitely many, a phenomenon called chattering; this can be problematic for existing motion planning algorithms that plan using a finite set of motion primitives. One remedy is to add some penalty for switching between controls. This paper explores the implications of this switching cost for optimal trajectories, using kinematic rigid bodies in the plane (which have been studied extensively in the cost-free-switch model) as an example system. Blatts Indifference Principle (BIP) is used to derive necessary conditions on optimal trajectories; Lipschitzian optimization techniques together with an A-star search yield an algorithm for finding trajectories that can arbitrarily approximate the optimal trajectories. We describe how to exploit the formation and storage of an embedded image thumbnail for image authentication. The creation of a thumbnail is modeled with a series of filtering operations, contrast adjustment, and compression. We automatically estimate these model parameters and show that these parameters differ significantly between camera manufacturers and photo-editing software. We also describe how this signature can be combined with encoding information from the underlying full resolution image to further refine the signatures distinctiveness. This paper presents an algorithm for folding a serial revolute chain into a rigid structure of essentially any desired planar shape. The algorithm is fast (linear in the number of links), and the constructed folding plan only requires an actuation method that sequentially folds triangles as the pattern is laid out, maintaining incremental rigidity of the structure during folding. Claims of a broader conspiracy behind U.S. President John F. Kennedys assassination have persisted for the past nearly five decades. The Zapruder film is considered to be the most complete recording of JFKs assassination. Many have claimed that this eigth millimeter film was manipulated to conceal evidence of a second shooter, which would invalidate the claim that a lone gunman, Lee Harvey Oswald, was responsible for JFKs assassination. Here we consider the viability of one specific claim of postproduction tampering in the Zapruder film. We show that using a fixture-based approach, knots can be tightened satisfying fairly precise geometric constraints; for example, we might like the loops of tied shoelaces or a decorative cloverleaf knot to each be some precise length. A robot arm and specially designed gripper are used first to arrange knots on the fixture, comprised of a collection of straight rods. Some of the rods can move; precise tightening is achieved by pulling of the open ends of the string, while rods guide and delay friction locks appropriately. We show an algorithm for designing a fixture based on an arbitrary input knot diagram. Some example knots, including the cloverleaf knot, are tied as a proof of concept.