* Hough transform

** Arbitrary shapes ( generalized Hough transform )

* Hough transform for detecting straight lines, circles or ellipses from edge points

The Hough transform () is a feature extraction technique used in image analysis, computer vision, and digital image processing.

This voting procedure is carried out in a parameter space, from which object candidates are obtained as local maxima in a so-called accumulator space that is explicitly constructed by the algorithm for computing the Hough transform.

The classical Hough transform was concerned with the identification of lines in the image, but later the Hough transform has been extended to identifying positions of arbitrary shapes, most commonly circles or ellipses.

The Hough transform as it is universally used today was invented by Richard Duda and Peter Hart in 1972, who called it a " generalized Hough transform " after the related 1962 patent of Paul Hough.

The transform was popularized in the computer vision community by Dana H. Ballard through a 1981 journal article titled " Generalizing the Hough transform to detect arbitrary shapes ".

The purpose of the Hough transform is to address this problem by making it possible to perform groupings of edge points into object candidates by performing an explicit voting procedure over a set of parameterized image objects ( Shapiro and Stockman, 304 ).

The simplest case of Hough transform is the linear transform for detecting straight lines.

In the Hough transform, a main idea is to consider the characteristics of the straight line not as image points ( x < sub > 1 </ sub >, y < sub > 1 </ sub >), ( x < sub > 2 </ sub >, y < sub > 2 </ sub >), etc., but instead, in terms of its parameters, i. e., the slope parameter m and the intercept parameter b. Based on that fact, the straight line y = mx + b can be represented as a point ( b, m ) in the parameter space.

However, one faces the problem that vertical lines give rise to unbounded values of the parameters m and b. For computational reasons, it is therefore better to use a different pair of parameters, denoted and ( theta ), for the lines in the Hough transform.

This representation makes the Hough transform conceptually very close to the two-dimensional Radon transform.

* The Hough transform, when written in a continuous form, is very similar, if not equivalent, to the Radon transform.

`` It is a duty '', said Hough, `` not to let pass this opportunity of protesting against the methods of taking and printing testimony in Equity, current in this circuit ( and probably others ), excused if not justified by the rules of the Supreme Court, especially to be found in patent causes, and flagrantly exemplified in this litigation.

The fundamental difficulty of which the Selden case was `` a striking ( though not singular ) example '', concluded Hough, `` will remain as long as testimony is taken without any authoritative judicial officer present, and responsible for the maintenance of discipline, and the reception or exclusion of testimony ''.

J. N. Hough suggests that Plautus ’ s use of Greek is for artistic purposes and not simply because a Latin phrase will not fit the meter.

The University of Louisiana-Monroe owns a one-hundred acre outdoor classroom, located near Hough Bend, that is used primarily for tree identification.

* Hough's Neck is a northeastern peninsular community named for Atherton Hough, who was granted the land in 1636 for use as a farm and orchard.

Huntersville is served by Charlotte-Mecklenburg Schools, with students from Huntersville attending Hough High School ( which opened in the fall of 2010 ), Hopewell High School and North Mecklenburg High School.

'< p >" Over three centuries later, Walter Hough ( 1912 ) wrote: ' There is a great confusion as to the identity of copal, the name, according to some writers, being used to cover a number of gums.

Phillips is presently reported to be in a relationship with US show jumping rider Lauren Hough, at 35 some four months younger than his son.

When the coefficients are separated into their height and latitude components, the height dependence takes the form of propagating or evanescent waves ( depending on conditions ), while the latitude dependence is given by the Hough functions.

The ( r, θ ) plane is sometimes referred to as Hough space for the set of straight lines in two dimensions.

where s is the distance of L from the origin and is the angle the normal vector to L makes with the x axis ( see also Hough space ).

The first hoop skirt in the US is from 1846, patent number 4, 584 of David Hough, Jr.

Delayed onset muscle soreness was first described in 1902 by Theodore Hough, who concluded that this kind of soreness is " fundamentally the result of ruptures within the muscle ".

In contrast to the previous searches, here the matched-filtering results from 84 data segments of 25 hours each, from both 4-km LIGO Hanford and Livingston instruments, were already combined on the volunteers ' computers via a Hough transform technique.

Each Hough mode is a function of latitude and may be expressed as an infinite sum of associated Legendre polynomials ; the functions are orthogonal over the sphere in the continuous case.

It will be recalled that in his summation for the A.L.A.M. before Judge Hough, Fish had condemned patent litigation as the curse of the American industrial community.

While Jerry F. Hough agrees with Daniels analysis, he states that other factors must be included ; for example an official with a bad relationship with the General Secretary would not be appointed to the Central Committee.

All of Alexandra's children were apparently born prematurely ; biographer Richard Hough thought Alexandra deliberately misled Queen Victoria as to her probable delivery dates, as she did not want the Queen to be present at their births.

Coal has been mined in the area since medieval times and mine workings from these times can be found on the Hough Mill site at Swannington near the Califat Colliery site.

A life-sized horse gin has been built on the Hough Mill site and craters can be seen in the ground, where the medieval villagers dug out their allocation of coal.

For instance, Hough End Crescent was meant to be an arc of very large houses, linking the ends of Alexandra and Withington Roads.

Hough had directed a horror film for Nicholson at AIP, and could bring English actress Susan George into the mix, providing one of the male leads would be rewritten for her.

Parker was ill, perhaps dying, and desired to be admitted by proxy ; but the fellows refused to elect him, having already elected John Hough.

Although the station is outside the metropolitan county of Merseyside, tickets issued by Merseytravel ( which usually can only be used within Merseyside ) are valid for travel to and from Hough Green.

On February 11, 1899, Francis filed an application for copyright of his painting “ Dog Looking At and Listening to a Phonograph .” Thinking the Edison-Bell Company located in New Jersey, USA, might find it useful, he presented it to James E. Hough, who promptly said, “ Dogs don ’ t listen to phonographs .” On May 31, 1899, Barraud went to the Maiden Lane offices of The Gramophone Company with the intention of borrowing a brass horn to replace the original black horn on the painting.

Heading into North Barrington, the road continues its journey as it crosses paths with Illinois Route 59 ( Hough Street ) until soon after, when it nears the more densely populated area of

Julianne Hough became the youngest professional dancer in Dancing with the Stars in the United States when she danced with the speed skater Apolo Anton Ohno during Season four at the age of 18.