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Indoor localization using fine time measurement (FTM) round-trip time (RTT) with respect to cooperating Wi-Fi access points (APs) has been shown to work well and provide 1–2 m accuracy in both 2D and 3D applications. This approach depends... more
Indoor localization using fine time measurement (FTM) round-trip time (RTT) with respect to cooperating Wi-Fi access points (APs) has been shown to work well and provide 1–2 m accuracy in both 2D and 3D applications. This approach depends on APs implementing the IEEE 802.11-2016 (also known as IEEE 802.11mc) Wi-Fi standard (“two-sided” RTT). Unfortunately, the penetration of this Wi-Fi protocol has been slower than anticipated, perhaps because APs tend not to be upgraded as often as other kinds of electronics, in particular in large institutions—where they would be most useful. Recently, Google released Android 12, which also supports an alternative “one-sided” RTT method that will work with legacy APs as well. This method cannot subtract out the “turn-around” time of the signal, and so, produces distance estimates that have much larger offsets than those seen with two-sided RTT—and the results are somewhat less accurate. At the same time, this method makes possible distance measure...
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It is well known that a function can be decomposed uniquely into the sum of an odd and an even function. This notion can be extended to the unique decomposition into the sum of four functions — two of which are even and two odd. These... more
It is well known that a function can be decomposed uniquely into the sum of an odd and an even function. This notion can be extended to the unique decomposition into the sum of four functions — two of which are even and two odd. These four functions are eigenvectors of the Fourier Transform with four different eigenvalues. That is, the Fourier transform of each of the four components is simply that component multiplied by the corresponding eigenvalue. Some eigenvectors of the discrete Fourier transform of particular interest find application in coding, communication and imaging. Some of the underlying mathematics goes back to the times of Carl Friedrich Gauss.
Convolutions have long been regarded as fundamental to applied mathematics, physics and engineering. Their mathematical elegance allows for common tasks such as numerical differentiation to be computed efficiently on large data sets.... more
Convolutions have long been regarded as fundamental to applied mathematics, physics and engineering. Their mathematical elegance allows for common tasks such as numerical differentiation to be computed efficiently on large data sets. Efficient computation of convolutions is critical to artificial intelligence in real-time applications, like machine vision, where convolutions must be continuously and efficiently computed on tens to hundreds of kilobytes per second. In this paper, we explore how convolutions are used in fundamental machine vision applications. We present an accelerated n-dimensional convolution package in the high performance computing language, Julia, and demonstrate its efficacy in solving the time to contact problem for machine vision. Results are measured against synthetically generated videos and quantitatively assessed according to their mean squared error from the ground truth. We achieve over an order of magnitude decrease in compute time and allocated memory ...
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This paper briefly describes the processing performed in the course of producing a line drawing from vidisector information. MIT Artificial Intelligence Laboratory Vision Group
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Bilateral cruise control (BCC) suppresses traffic flow instabilities. Previously, for simplicity of analysis, vehicles in BCC traffic flow were assumed to be identical, i.e., using the same gains for control. In this study, we analyze the... more
Bilateral cruise control (BCC) suppresses traffic flow instabilities. Previously, for simplicity of analysis, vehicles in BCC traffic flow were assumed to be identical, i.e., using the same gains for control. In this study, we analyze the stability of an inhomogeneous vehicular chain in which the gains used by different vehicles are not the same. Not unexpectedly, mathematical analysis becomes more difficult, and leads to a quadratic eigenvalue problem. We study several different cases, and shows that a chain of vehicles under bilateral cruise control is stable even when the vehicles do not all have the same control system properties. Numerical simulations validate the analysis.
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In this paper, we study the chain stability of vehicles under bilateral control (BCM), and prove that vehicles under bilateral control are chain stable, i.e., all input perturbations to the chain decay exponentially (with the length of... more
In this paper, we study the chain stability of vehicles under bilateral control (BCM), and prove that vehicles under bilateral control are chain stable, i.e., all input perturbations to the chain decay exponentially (with the length of the chain). Chain stability analysis tells us how vehicles under bilateral control will act in traffic when mixed with cars driven by human drivers. It shows that self-driving cars using bilateral control can reduce traffic flow instabilities in mixed traffic. Indeed, chains of BCM vehicles become perturbation-consuming dampers when inserted in traffic, since they split chains of human-driven vehicles and prevent perturbations from being transmitted from one chain of car-following cars to the next. Thus, today's traffic can be improved greatly by the insertion of BCM vehicles. The simulation results validate the theoretical analysis.
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In this paper, we present a method of detecting the rail track bends and flaws. Different from the traditional machine-vision based methods which analyze the images of the rail surface, we estimate the shake of the camera - which is... more
In this paper, we present a method of detecting the rail track bends and flaws. Different from the traditional machine-vision based methods which analyze the images of the rail surface, we estimate the shake of the camera - which is caused by the flaw or bend of the rail track - from the video used for railway environment surveillance. We provide both theoretical analysis - based on the theory of optical flow and passive navigation - and the corresponding fast algorithms, i.e. the brightness-pattern-matching code (BPMC) and shaking-type code (STC). Our method uses the surveillance video of the railway environment directly, thus, we do not need extra expensive instruments.
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We have developed a versatile instrument for in situ measurement of motions of MEMS. Images of MEMS are magnified with an optical microscope and projected onto a CCD camera. Stroboscopic illumination is used to obtain stop-action images... more
We have developed a versatile instrument for in situ measurement of motions of MEMS. Images of MEMS are magnified with an optical microscope and projected onto a CCD camera. Stroboscopic illumination is used to obtain stop-action images of the moving structures. Stopaction images from multiple focal planes provide information about 3D structure and 3D motion. Image analysis algorithms determine motions of all visible structures with nanometer accuracy.Hardware for the system includes the microscope, CCD camera and associated frame grabber, piezoelectric focusing element, and a modular stimulator that generates arbitrary periodic waveforms and synchronized stroboscopic illumination. These elements are controlled from a Pentium-based computer using a graphical user interface that guides the user through both data collection and data analysis. The system can measure motions at frequencies as high as 5 MHz with nanometer resolution, i.e., well below the wavelength of light.
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Abstract—This paper proposes hypothetical guidelines for identifying applications which are more suitable for analog VLSI (Very Large Scale Integration) chip implementations rather than conventional digital approaches. Significant merits... more
Abstract—This paper proposes hypothetical guidelines for identifying applications which are more suitable for analog VLSI (Very Large Scale Integration) chip implementations rather than conventional digital approaches. Significant merits are realized when new ...
Novel algorithms for object recognition are described that directly recover the transformations relating the image to its model. Unlike methods fitting the conventional framework, these new methods do not require exhaustive search for... more
Novel algorithms for object recognition are described that directly recover the transformations relating the image to its model. Unlike methods fitting the conventional framework, these new methods do not require exhaustive search for each feature correspondence in order to solve for the transformation. Yet they allow simultaneous object identification and recovery of the transformation. Given hypothesized corresponding regions in the
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The Raytheon Trimodal Imager (TMI) uses coded aperture and Compton imaging technologies as well as the nonimaging shadow technology to locate an SNM or radiological threat in the presence of background. The coded aperture imaging is... more
The Raytheon Trimodal Imager (TMI) uses coded aperture and Compton imaging technologies as well as the nonimaging shadow technology to locate an SNM or radiological threat in the presence of background. The coded aperture imaging is useful for locating and ...
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... Later on the board must be inspected again after wave soldering , again with many hand corrections necessary . The Japanes e ... Page 10. BERTHOLD K . P. HORN 9 LEAD BONDING REFERENCES ... Mini - Compute r (PDP11) B/W Monito r... more
... Later on the board must be inspected again after wave soldering , again with many hand corrections necessary . The Japanes e ... Page 10. BERTHOLD K . P. HORN 9 LEAD BONDING REFERENCES ... Mini - Compute r (PDP11) B/W Monito r Standard Vidico n Camera Head ...
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Dr. Andrew Lumsdaine,' Dr. Ichiro Masaki,2 Dr. Herre SJ van der Zant, Dr. He Yie3 ... Mazhar M. Alidina, Donald G. Baltus, Vishal L. Bhagwati, Xuejun Cai, Michael Chou, Steven J. Decker, Lisa G. Dron, Ibrahim... more
Dr. Andrew Lumsdaine,' Dr. Ichiro Masaki,2 Dr. Herre SJ van der Zant, Dr. He Yie3 ... Mazhar M. Alidina, Donald G. Baltus, Vishal L. Bhagwati, Xuejun Cai, Michael Chou, Steven J. Decker, Lisa G. Dron, Ibrahim M. Elfadel, J. Mikko Hakkarainen, Frederick P. Herrmann, ...
The IEEE 802.11mc WiFi standard provides a protocol for a cellphone to measure its distance from WiFi access points (APs). The position of the cellphone can then be estimated from the reported distances using known positions of the APs.... more
The IEEE 802.11mc WiFi standard provides a protocol for a cellphone to measure its distance from WiFi access points (APs). The position of the cellphone can then be estimated from the reported distances using known positions of the APs. There are several “multilateration” methods that work in relatively open environments. The problem is harder in a typical residence where signals pass through walls and floors. There, Bayesian cell update has shown particular promise. The Bayesian grid update method requires an “observation model” which gives the conditional probability of observing a reported distance given a known actual distance. The parameters of an observation model may be fitted using scattergrams of reported distances versus actual distance. We show here that the problem of fitting an observation model can be reduced from two dimensions to one. We further show that, perhaps surprisingly, a “double exponential” observation model fits real data well. Generating the test data inv...
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Determination of indoor position based on fine time measurement (FTM) of the round trip time (RTT) of a signal between an initiator (smartphone) and a responder (Wi-Fi access point) enables a number of applications. However, the accuracy... more
Determination of indoor position based on fine time measurement (FTM) of the round trip time (RTT) of a signal between an initiator (smartphone) and a responder (Wi-Fi access point) enables a number of applications. However, the accuracy currently attainable—standard deviations of 1–2 m in distance measurement under favorable circumstances—limits the range of possible applications. An emergency worker, for example, may not be able to unequivocally determine on which floor someone in need of help is in a multi-story building. The error in position depends on several factors, including the bandwidth of the RF signal, delay of the signal due to the high relative permittivity of construction materials, and the geometry-dependent “noise gain” of position determination. Errors in distance measurements have unusal properties that are exposed here. Improvements in accuracy depend on understanding all of these error sources. This paper introduces “frequency diversity,” a method for doubling ...
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The MIT AI Laboratory has a long tradition of research in most aspects of Artificial Intelligence. Currently, the major foci include computer vision, manipulation, learning, English-language understanding, VLSI design, expert engineering... more
The MIT AI Laboratory has a long tradition of research in most aspects of Artificial Intelligence. Currently, the major foci include computer vision, manipulation, learning, English-language understanding, VLSI design, expert engineering problem solving, common-sense reasoning, computer architecture, distributed problem solving, models of human memory, programmer apprentices, and human education.
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ABSTRACT Traffic flow instabilities have many potential negative consequences, including increased danger of collisions, higher fuel consumption, faster of abrasion of roadways, and reduction of overall traffic throughput. Instabilities... more
ABSTRACT Traffic flow instabilities have many potential negative consequences, including increased danger of collisions, higher fuel consumption, faster of abrasion of roadways, and reduction of overall traffic throughput. Instabilities occur even if modern forward-looking adaptive cruise control systems are used. In this paper, we present an architecture for controlling vehicle density that uses coordination between adjacent vehicles to attain desired safe following distances, without generating these types of instabilities in the process. The presented architecture has several additional desirable properties, including being robust to sensor failures and measurement inconsistencies, as well as allowing for inhomogeneous vehicle dynamics.
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ABSTRACT Coded aperture techniques based on a cyclic difference set uniformly redundant array (URA) can increase sensitivity of an imaging system without degrading the spatial resolution. In this paper, we discuss the pattern design and... more
ABSTRACT Coded aperture techniques based on a cyclic difference set uniformly redundant array (URA) can increase sensitivity of an imaging system without degrading the spatial resolution. In this paper, we discuss the pattern design and present its application for diagnostic nuclear medicine imaging with experimental results. Point-like, planar, and three- dimensional 140 keV gamma-ray sources are used in our experiments. We have experimentally demonstrated a three- dimensional coded aperture technique for nuclear medicine imaging and have compared it with conventional collimator systems.
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Research Interests: Automata Theory and Chip
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ABSTRACT Accurate air temperature observations are important for urban meteorology, for example to study the urban heat island and adverse effects of high temperatures on human health. The number of available temperature observations is... more
ABSTRACT Accurate air temperature observations are important for urban meteorology, for example to study the urban heat island and adverse effects of high temperatures on human health. The number of available temperature observations is often relatively limited. A new development is presented to derive temperature information for the urban canopy from an alternative source: cell phones. Battery temperature data were collected by users of an Android application for cell phones (opensignal.com). The application automatically sends battery temperature data to a server for storage. In this study, battery temperatures are averaged in space and time to obtain daily averaged battery temperatures for each city separately. A regression model, which can be related to a physical model, is employed to retrieve daily air temperatures from battery temperatures. The model is calibrated with observed air temperatures from a meteorological station of an airport located in or near the city. Time series of air temperatures are obtained for each city for a period of several months, where 50% of the data is for independent verification. Results are presented for Buenos Aires, London, Los Angeles, Paris, Mexico City, Moscow, Rome, and Sao Paulo. The evolution of the retrieved air temperatures often correspond well with the observed ones. The mean absolute error of daily air temperatures is less than 2 degrees Celsius, and the bias is within 1 degree Celsius. This shows that monitoring air temperatures employing an Android application holds great promise. Since 75% of the world's population has a cell phone, 20% of the land surface of the earth has cellular telephone coverage, and 500 million devices use the Android operating system, there is a huge potential for measuring air temperatures employing cell phones. This could eventually lead to real-time world-wide temperature maps.
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Page 1. Coded Source Imaging for Neutrons and X-Rays Antonio L Damato, Berthold KP Horn and Richard C. Lanza, Member, IEEE Abstract X-ray and neutron imaging techniques are powerful tools applied to a wide array ...
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Describes a project to design and build prototype analog early vision systems to determine how the advantages of analog VLSI, high speed, low power, and small area, can be exploited and its disadvantages, limited accuracy, inflexibility,... more
Describes a project to design and build prototype analog early vision systems to determine how the advantages of analog VLSI, high speed, low power, and small area, can be exploited and its disadvantages, limited accuracy, inflexibility, lack of storage capacity, and long design times, can be minimized. This project explored three distinct circuit design styles for vision applications, continuous-time processing,
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Describes a project to design and build prototype analog early vision systems that are remarkably low power, small, and fast. This paper briefly outlines the overall effort and describes three chips in some detail
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A small but very efficient X-ray detector operating in a current integrating mode for use in high speed tomography apparatus comprises a scintillator that is entirely coated with a highly reflective matte material except for a relatively... more
A small but very efficient X-ray detector operating in a current integrating mode for use in high speed tomography apparatus comprises a scintillator that is entirely coated with a highly reflective matte material except for a relatively small-area window. A PIN photodiode is juxtaposed with the scintillator opposite the window and the two are secured together at an optical interface comprising a transparent adherent material preferably having an index of refraction between the indices of the scintillator and the photo-diode. The ratio of the active surface area of the photo-diode to the area of the scintillator coated with reflective material is appreciably less than unity. 11 claims.
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The brightness patterns in two successive im age frames are used to recover the motion of a planar ob ject without computing the optical flow as an intermediate step. Based on a least-squares formulation, a set of nine nonlinear... more
The brightness patterns in two successive im age frames are used to recover the motion of a planar ob ject without computing the optical flow as an intermediate step. Based on a least-squares formulation, a set of nine nonlinear equations are derived. A simple iterative scheme for solving these equations is presented. Using a selected example, it is shown that in general, the scheme may con verge to cither of two possible solutions depending on the initial condition. Only in the special case where the trans- lational motion vector is perpendicular to the surface does our algorithm converge to a unique solution.
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Abstract: Finding,the relationship,between,two,coordinate,systems,us- ing pairs of measurements,of the coordinates of a number of points in both systems is a classic photogrammetric,task. It finds applications in stereophotogrammetry... more
Abstract: Finding,the relationship,between,two,coordinate,systems,us- ing pairs of measurements,of the coordinates of a number of points in both systems is a classic photogrammetric,task. It finds applications in stereophotogrammetry and,in robotics.,We present,here,a closed-form solution,to the,least-squares,problem,for three,or,more,points.,Cur- rently, various empirical, graphical and numerical iterative methods are in use. Derivation,of a closed-form,solution,can,be,simplified,by,using unit quaternions to represent rotation, as was shown in an earlier paper,. Since orthonormal matrices are more widely used to represent rotation, we,now,present,a solution,using,3 × 3 matrices.,Our method,requires,the computation,of the square-root,of a symmetric,matrix. We compare,the new,result with,an alternate,method,where,orthonormality,is not directly enforced.,In this other,method,a best,fit linear,transformation,is found and,then,the nearest,orthonormal,matrix,chosen,for the rotation.
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Page 1. HaB$aEHU$ETTS INETITUTE UP TEEHWULUGE FRHJEUT HAG Artificial Intelligence Henc. Ha. 1?H August 1969 The Image Diaaectnr 'eyea' BKP Hnrn This ia a cnllectinn nf data an the cnnatructinn nperaticn and... more
Page 1. HaB$aEHU$ETTS INETITUTE UP TEEHWULUGE FRHJEUT HAG Artificial Intelligence Henc. Ha. 1?H August 1969 The Image Diaaectnr 'eyea' BKP Hnrn This ia a cnllectinn nf data an the cnnatructinn nperaticn and perfarmance cf the tun image diaaactur cameraa. ...
In the course of designing an integrated system for locating the focus of expansion (FOE) from a sequence of images taken while a camera is translating, a variety of direct motion vision algorithms based on image brightness gradients have... more
In the course of designing an integrated system for locating the focus of expansion (FOE) from a sequence of images taken while a camera is translating, a variety of direct motion vision algorithms based on image brightness gradients have been studied (McQuirk, 1991, 1996b). The location of the FOE is the intersection of the translation vector of the camera with
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... and so (£3) x F = (13^3^ - (^'l11 (EZ + ^3) x E = (^iz + 13clZ3>v - (^iz + ^iza^ (ri + Cz + r3) x F = (liCi + I^IZ + 13t:lZ3)v - (^l + ^12 + ^IZS1" This can be written in matrix form.... more
... and so (£3) x F = (13^3^ - (^'l11 (EZ + ^3) x E = (^iz + 13clZ3>v - (^iz + ^iza^ (ri + Cz + r3) x F = (liCi + I^IZ + 13t:lZ3)v - (^l + ^12 + ^IZS1" This can be written in matrix form. Page 24. ... Horn -diSi + l^ig + LjSi^) -(^iz + 13^3) -(^iza) di Ci + l;,ci;, * 130123) 1 dzCiz + 130123) 1 (^iza) 1. ...
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Page 1. Analysis of Surface Area Estimates of Binary Vol-umes Under Three Tilings Erik G. Miller Learning & Vision Group Artificial Intelligence Laboratory Massachusetts Institue Of Technology The Problem: To represent images ...
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Page 1. $¿*m\ Massachusetts Institute of Technology Artificial Intelligence Laboratory AI Memo No. 726 May, 1983 Picking up an object from a pile of objects Katsushi Ikeuchi, Berthold KP Horn, Shigemi Nagata Tom Callahan ...
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Research Interests: Algorithms, Image Processing, Optical Flow, Navigation, Change detection, and 13 moreOptical computing, Motion, Eigenvalues, Velocity, Matrix Decomposition, Intensity, Reciprocally Symmetric Matrices, Rotation, Vector Analysis, Brightness, Least squares method, Eigenvalue Decomposition, and Symmetric Matrices
First two chapters of textbook on machine vision. (Also available in Russian, Japanese and Chinese translations).
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Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics.... more
Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closed-form solution to the least-squares problem for three or more points. Currently various empirical, graphical, and numerical iterative methods are in use. Derivation of the solution is simplified by use of unit quaternions to represent rotation. I emphasize a symmetry property that a solution to this problem ought to possess. The best translational offset is the difference between the centroid of the coordinates in one system and the rotated and scaled centroid of the coordinates in the other system. The best scale is equal to the ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 X 4 matrix. The elements of this matrix are combinations of sums of products of corresponding
coordinates of the points
coordinates of the points
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The Energy Citations Database (ECD) provides access to historical and current research (1948 to the present) from the Department of Energy (DOE) and predecessor agencies.
An image of a smooth object known to have a uniform surface will exhibit gradations of reflected light intensity which can be used to determine its shape. This is not obvious since at each point in the image we know only the reflectivity... more
An image of a smooth object known to have a uniform surface will exhibit gradations of reflected light intensity which can be used to determine its shape. This is not obvious since at each point in the image we know only the reflectivity at the corresponding object point. For some points (called singular points here) the reflectivity does uniquely determine the local normal, but for
almost all points it does not. Consequently, the shape of the surface cannot be found by local operations alone
almost all points it does not. Consequently, the shape of the surface cannot be found by local operations alone
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Research Interests: Computer Vision, Calculus of Variations, Digital Elevation Models, Models, Variational Methods, and 13 moreDigital Elevation Model, RADIANCE, Perforation, Reflectance, Calculus of Variation, Elevation, Shape from Shading, Height, Boundary Condition, Linearity, Synthetic Data Generation, Singular Point, and Exact solution methods
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A method for the determination of lightness from image intensity is presented. For certain classes ot images, lightness corresponds to reflectance, while image intensity is the product of reflectance and illumination intensity. The method... more
A method for the determination of lightness from image intensity is presented. For certain classes ot images, lightness corresponds to reflectance, while image intensity is the product of reflectance and illumination intensity. The method is two-dimensional and depends on the different spatial distribution of these two components of image intensity. Such a lightness-judging process is required for Land's retinex theory of color vision. A number of physical models are developed and computer simulation of the process is demonstrated. This work should be of interest to designers of image processing hardware, cognitive psychologists dealing with the human visual system, and neurophysiologists concerned with the function of structures in the primate retina.
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Research Interests: Mechanical Engineering, Optics, Image Processing, Medical Imaging, Fiber Optics, and 12 moreTelecommunications, Photonics, Machine Vision, Society, Optical, Artificial Intelligent, Light, Applied Optics, Optical physics, Department of Defense, Electrical And Electronic Engineering, and Image Formation
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Relative orientation is the recovery of the position and orientation of one imaging system relative to another from correspondences among five or more ray pairs. It is one of four core problems in photogrammetry and is of central... more
Relative orientation is the recovery of the position and orientation of one imaging system relative to another from correspondences among five or more ray pairs. It is one of four core problems in photogrammetry and is of central importance in binocular stereo as well as in long-range motion vision. While five ray correspondences are sufficient to yield a finite number of solutions, more than five correspondences are used in practice
to ensure an accurate solution with least-squares methods. Most iterative schemes for minimizmg the sum of the squares of weighted errors require a good guess as a starting value. The author has previously published a method that results in the best solution without requiring an initial guess [J. Opt. Soc. Am. A 4, 629 (1987)]. An even simpler method is presented here that utilizes the representation of rotations by unit quaternions.
to ensure an accurate solution with least-squares methods. Most iterative schemes for minimizmg the sum of the squares of weighted errors require a good guess as a starting value. The author has previously published a method that results in the best solution without requiring an initial guess [J. Opt. Soc. Am. A 4, 629 (1987)]. An even simpler method is presented here that utilizes the representation of rotations by unit quaternions.
Research Interests: Optics, Computer Vision, Medical Imaging, Photogrammetry, Fiber Optics, and 15 moreTelecommunications, Imaging, Photonics, Society, Orientation, Optical, Light, Long Range, Measurement Error, Optical physics, Optometry and Ophthalmology, Electrical And Electronic Engineering, Least Square Method, sum of two squares, and Least squares method
This memo describes a method of automatically focusing the new vidisector (TVC). The same method can be used for distance measuring. Included are instructions describing the use of a special LISP and the required LISP-functions. The use... more
This memo describes a method of automatically focusing the new vidisector (TVC). The same method can be used for distance measuring. Included are instructions describing the use of a special LISP and the required LISP-functions. The use of the vidisectors, as well ...
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Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical... more
Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent
velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather
coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.
velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather
coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.
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The use of rotationally symmetric operators in vision is reviewed and conditions for rotational symmetry are derived for linear and quadratic forms in the first and second partial directional derivatives of a function f ( x , y). Surface... more
The use of rotationally symmetric operators in vision is reviewed and conditions for rotational symmetry are derived for linear and quadratic forms in the first and second partial directional derivatives of a function f ( x , y). Surface interpolation is considered to be the process of computing the most conservative solution consistent with boundary conditions. The " most conservative" solution is modeled using the calculus of variations to find the minimum function that satisfies a given performance index. To guarantee the existence of a minimum function, Grimson (W. E. L. Grimson, From Images to Surfaces: A Computational Study of the Human Early Visual System, MIT Press: Cambridge, Mass., 1981.) has recently suggested that
the performance index should be a seminorm. It is shown that all quadratic forms in the second partial derivatives of the surface satisfy this criterion. The seminorms that are, in addition,
rotationally symmetric form a vector space whose basis is the square Laplacian and the quadratic variation. Whereas both seminorms give rise to the same Euler condition in the
interior, the quadratic variation offers the tighter constraint at the boundary and is to be preferred for surface interpolation
the performance index should be a seminorm. It is shown that all quadratic forms in the second partial derivatives of the surface satisfy this criterion. The seminorms that are, in addition,
rotationally symmetric form a vector space whose basis is the square Laplacian and the quadratic variation. Whereas both seminorms give rise to the same Euler condition in the
interior, the quadratic variation offers the tighter constraint at the boundary and is to be preferred for surface interpolation
Research Interests: Computer Graphics, Artificial Intelligence, Image Processing, Calculus of Variations, Pattern Recognition, and 13 moreInformation Processing, Vision, Process Simulation, Computer Graphics and Image Processing, Interpolation, Computer Graphic, Calculus of Variation, Boolean Satisfiability, Vector Space, Boundary Condition, Numerical Solution, Quadratic Variation, and Performance Index
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In order to improve the safety of night driving, automatic pedestrian detection has received more and more attraction. Since reliability is the most important issue in these systems, multi-dimensional-feature-based segmentation and... more
In order to improve the safety of night driving, automatic pedestrian detection has received more and more attraction. Since reliability is the most important issue in these systems, multi-dimensional-feature-based segmentation and classification needs to be introduced, ...
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The essential matrix is primarily of theoretical interest, since it is at best useful only when exactly five ray correspondences have been found. In practice one typically applies least-squares methods to many more than five ray pairs in... more
The essential matrix is primarily of theoretical interest, since it is at best useful only when exactly five ray correspondences have been found. In practice one typically applies least-squares methods to many more than five ray pairs in order to attain good accuracy [Zeller 52] [Ghosh 72] [Slama et al. 80] [Wolf 83] [Horn 86, 87b]. If one has more than five ray correspondences, one could try and use least-squares methods to find a “best-fit” essential matrix, provided one could enforces three non-linear conditions that ensure that the matrix is decomposable. This has not proven feasible. If, on the other hand, the three conditions are not enforced, then the resulting matrix will not be decomposable, and the methods described here (or elsewhere) should not be applied, since the elements of the matrix are then inconsistent. Applying an algorithm that assumes that the data is consistent can in this case lead to very poor results. At the very least, one should try to find a baseline and a rotation that yields an essential matrix as close as possible in the least-squares sense to the given inconsistent matrix. This too is a difficult problem
Research Interests:
Research Interests:
Constraints on optical flow computation(for image planes). BG SCHUNCK, BKP HORN Conference on Pattern Recognition and Image Processing, Dallas, TX, 205-210, 1981. A motion constraint equation is devised to relate ...
Research Interests:
Basic camera calibration is the recovery of the principle distance f and the principle point (x0, y0) in the image plane — or, equivalently, recovery of the position of the center of projection (x0, y0, f ) in the image coordinate system.... more
Basic camera calibration is the recovery of the principle distance f and the principle point (x0, y0) in the image plane — or, equivalently, recovery of the position of the center of projection (x0, y0, f ) in the image coordinate system. This is
referred to as interior orientation in photogrammetry.
A calibration target can be imaged to provide correspondences between points in the image and points in space. It is, however, generally impractical to position the calibration target accurately with respect to the camera coordinate system using only mechanical means. As a result, the relationship between the
target coordinate system and the camera coordinate system typically also needs to be recovered from the correspondences. This is referred to as exterior orientation in photogrammetry.
referred to as interior orientation in photogrammetry.
A calibration target can be imaged to provide correspondences between points in the image and points in space. It is, however, generally impractical to position the calibration target accurately with respect to the camera coordinate system using only mechanical means. As a result, the relationship between the
target coordinate system and the camera coordinate system typically also needs to be recovered from the correspondences. This is referred to as exterior orientation in photogrammetry.
Research Interests:
AbstractDynamic environment interpretation is of special interest for intelligent vehicle systems. It is expected to provide lane information, target depth, and the image positions of targets within given depth ranges. Typical... more
AbstractDynamic environment interpretation is of special interest for intelligent vehicle systems. It is expected to provide lane information, target depth, and the image positions of targets within given depth ranges. Typical segmentation algorithms cannot solve the problems ...