Berthold Horn

Massachusetts Institute of Technology (MIT), Electrical Engineering and Computer Science, Faculty Member

Followers

231

Following

Public Views

InterestsView All (9)

Uploads

Papers by Berthold Horn

The Intelligence of Cells

Science News, 1979

Method and Apparatus for Motion Estimation in Video Image Data

Indoor Localization Using Uncooperative Wi-Fi Access Points

Sensors

Indoor localization using fine time measurement (FTM) round-trip time (RTT) with respect to coope... 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...

Download

"Determining optical flow": a retrospective

Download

Font Forum ‘Hinting ’ of

Download

Eigenvectors of the Fourier Transform

It is well known that a function can be decomposed uniquely into the sum of an odd and an even fu... 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.

Download

Accelerated Convolutions for Efficient Multi-Scale Time to Contact Computation in Julia

Convolutions have long been regarded as fundamental to applied mathematics, physics and engineeri... 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 ...

Download

Quaternions: what are they, and why do we need to know?

Acta Crystallographica Section A Foundations and Advances, 2020

How should we represent rotations? Orthonormal (3 Â 3) matrices? Euler angles (pitch, yaw and rol... more How should we represent rotations? Orthonormal (3 Â 3) matrices? Euler angles (pitch, yaw and roll)? Axis and angle? Gibbs vector? Pauli (2 Â 2, complex) spin matrices? Cayley-Klein (complex) parameters? Euler-Rodrigues parameters? Hamilton's quaternions? Why are there so many choices (Goldstein, 1980; Varshalovich et al., 1988; Shuster, 1993)? We don't see this variety when it comes to translation: we just use vectors. The big difference is that translations live in a Euclidean vector space. Rotations do not, and so all the nice linear algebra machinery that we use for manipulating translations seems not to apply. Why does it matter how we represent rotation? Solving problems often depends on finding the 'right' representation. Sometimes a good notation can make it possible to solve a problem in closed form. Without a notion of the 'space of rotations' many problems are hard to formulate and solve. Spoiler alert: unit quaternions provide 'the' way to represent rotations. Why? Unit quaternions allow a clear visualization (see Hanson, 2006) of the space of rotations as the unit sphere S 3 in four dimensions (with antipodal points identified). Unit quaternions make it possible to differentiate an expression 'with respect to rotation'. Unit quaternions make it possible to find extrema of expressions by setting that derivative equal to zero! Unit quaternions make it easy to compose rotations (unlike, e.g., axis-and-angle notation). Unit quaternions do not suffer from singularities (as do, e.g., Euler angles when two axes line up-see gimbal lock). Unit quaternions, while redundant (four parameters for three degrees of freedom), have only one constraint on their components (unlike orthonormal matrices, which have six non-linear constraints on the rows or columns-plus one on the determinant). Unit quaternions make it possible to compute averages, to interpolate, to sample in the space of rotations and to represent densities over orientations. And, as demonstrated in Andrew Hanson's (2020) article in the previous issue of Acta Crystallographica Section A, they also make possible insightful illustrations relating to orientations. Which came first, the vector or the quaternion? Mathematicians extended algebra from real number to complex numbers. We can add, subtract, multiply and divide these. The question that obsessed Hamilton was whether there would be further generalizations to algebras with three components. His big breakthrough came when he realized it was not possible with three components-but it was possible with four (Hamilton, 1844)! That is how the quaternion was born-on 16 October 1843. Hamilton showed that for some applications in physics it was convenient to split the quaternion into a 'scalar' and a 'vector' part. For a few decades, quaternions were used in physics to represent spatial quantities, often with the scalar part set to zero. Maxwell used both notations in some of his work (Maxwell, 1873). Some got tired of using four components to represent positions in space which clearly only need three, and so lopped off the scalar component and switched to using just vectors. Gibbs and Heaviside were the main propagandizers of this approach (Crowe, 1967). The price they paid was that there is no algebra for vectors (e.g., no inverses with respect to multiplication). Some critics called vector analysis a 'hermaphrodite monster' because it 'compounded the notations of Hamilton and Grassmann' (Tait, 1867; Prichard, 1998). After an acrimonious war of words, the proponents of vectors finally won, and the rest is history.

Download

The Binford-Horn LINEFINDER

This paper briefly describes the processing performed in the course of producing a line drawing f... more

Download

Air temperature retrieval from crowd-sourced smartphone battery temperatures for Dutch cities and its application in mesoscale model validation

Download

David vs. Goliath?

Science News, 1986

Dodo Apocrypha

Science News, 1978

Stability analysis of a chain of non-identical vehicles under bilateral cruise control

Bilateral cruise control (BCC) suppresses traffic flow instabilities. Previously, for simplicity ... 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.

Download

On the chain stability of bilateral control model

IEEE Transactions on Automatic Control, 2019

In this paper, we study the chain stability of vehicles under bilateral control (BCM), and prove ... 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.

On the stability analysis of mixed traffic with vehicles under car-following and bilateral control

IEEE Transactions on Automatic Control, 2019

In this paper, we study a mixed traffic flow in which some cars are under car-following control a... more In this paper, we study a mixed traffic flow in which some cars are under car-following control and others are under bilateral control. We also provide the necessary (modular string) stability condition for this type of mixed traffic, which can be viewed as an extension of the condition for pure car-following control based traffic. This necessary stability condition provides some indication of how the introduction of self-driving cars (under bilateral control) will affect today's traffic.

Download

Detect the rail track flaw by estimating the camera shaking

17th International IEEE Conference on Intelligent Transportation Systems (ITSC), 2014

In this paper, we present a method of detecting the rail track bends and flaws. Different from th... 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.

Machine Vision to Alert Roadside Personnel of Night Traffic Threats

IEEE Transactions on Intelligent Transportation Systems, 2018

In the United States, every year, several people whose job takes them to the sides of roads, are ... more In the United States, every year, several people whose job takes them to the sides of roads, are injured or killed by roadside collisions. This could be avoided if a warning signal could be sent to them. In this paper, we describe a machinevision based alerting system which detects and tracks headlamps of cars in night traffic. The system automatically computes a "normal traffic" region in the image. Unusual trajectories of cars are detected when the images of their headlamps move out of that region. The system promptly sends a warning signal once a risk has been identified. The system runs on the Android smart phones, which are mounted on cars or on roadside fixtures.

Download

Advanced Vehicle Communication and Control Systems. Prospects for Cooperative Ivhs Operational Tests. Workshop Report

Schunck: Determining optical flow

Artificial Intelligence, 1981

Computer Microvision for MEMS

MRS Proceedings, 1999

We have developed a versatile instrument for in situ measurement of motions of MEMS. Images of ME... 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.

Download

Berthold Horn

Uploads

Papers by Berthold Horn

Log In