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## Lower order circle and ellipse hough transform (1997)

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### Other Repositories/Bibliography

Venue: | J. Pattern Recognition |

Citations: | 17 - 2 self |

### Citations

900 |
Use of the Hough transformation to detect lines and curves in pictures,”
- Duda, Hart
- 1972
(Show Context)
Citation Context ...computation I. INTRODUCTION Object recognition is one of the most frequent and necessary tasks in the realm of computer vision. The algorithms derived from the formulation of the Hough transform (HT) =-=(1)-=- have been shown as effective tools in order to achieve this objective. There are three types of figures to which special attention has been paid and for which specific algorithms that improve the det... |

482 | A survey of the Hough transform. - Illingworth, Kittler - 1988 |

62 |
Fast Hough transform: A hierarchical approach”,
- Li, Lavin, et al.
- 1986
(Show Context)
Citation Context ...maxima in the parameter space with a smaller computational and memory cost than the classical polling-search processes in the complete parameter space. (17-19) Among these focusing algorithms the FHT =-=(17)-=- stands out due to its regularity and ease of computation. However, it presents some drawbacks derived from the focusing strategy followed, which become more important when the image includes several ... |

51 |
Detection partially occluded ellipses using the Hough transform
- Yune, Illingworth, et al.
- 1989
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Citation Context ...oying a standard voting process on an accumulator space. All these works present problems in the case of partially hidden ellipses and, therefore, we will not consider them in Section 5.2. Yuen eta/. =-=(12)-=- solve the problem of detecting partially hidden ellipses by means of an algorithm that works in two stages. In the first stage they detect the centers and in the second they apply the Adaptive Hough ... |

46 | Data distributions for sparse matrix vector multiplication solvers. - Romero, Zapata - 1995 |

39 |
Detection of ellipses by a modified Hough transform.
- Tsuji, Matsumoto
- 1978
(Show Context)
Citation Context ...ellipse. In this stage, each line of the beam is defined by the normalized coefficients corresponding to equation (1): where A~lp 2 __ tim2 - t2ml APllP2 _ t2 - m2 F12 ~ [al2 A~lp 2 __ tl -- ml F12 , =-=(10)-=- Yl - Y2 - Xl~l +x2~2 t 1 = t2= ~2(1 (X2 -- X1) -- Y2~I + Yl~2 ~2 -~1 xl +x2 Yl +Y2 ml -- , m2 -- , 2 2 1~12 = ~/(t2 -- m2) 2 + (tl -- ml) 2. (11) The slopes of the points in the edge of the image are... |

31 | A Fast ellipse/circle detector using geometric symmetry
- Ho, Chen
- 1994
(Show Context)
Citation Context ...od to the points that make up each of the candidates. Tsukune and Goto (11) perform the detection in three stages using information from the gradient vectors of the points of the image edge. Ho eta/. =-=(16)-=- use two stages. In the first one, two symmetrical axes (vertical and horizontal) are extracted finding the midpoint of edge points scanned downwards and rightwards. The crosspoint of these two axes w... |

30 |
A modified Hough scheme for general circle location
- Davies
- 1988
(Show Context)
Citation Context ...ave completely extracted, but if the image has noise it is necessary to take larger window sizes. In Table 5 we display the computational complexity of these processes and the memory required. Davies =-=(21)-=- uses a stage for calculating the center voting in an N × N space and another stage for calculating the radii voting in a one-dimensional space. In the first stage the votes occur along the direction ... |

28 |
The dynamic generalized hough transform: its relationship to the probabilistic hough transforms and an application to the concurrent detection of circles and ellipses. CVGIP: Image understanding
- Leavers
- 1992
(Show Context)
Citation Context ...tion and complicating the center detection process. There are other methods based on windows that try to reduce the redundant information generated during the parametric transformation. So, the DGHT, =-=(22)-=- using geometric properties of the figures (circles and ellipses), makes a prior segmentation of them. After this process, the image is divided into several windows and only the feature points placed ... |

23 |
Multiresolution Hough transform-- an efficient method of detecting patterns in images
- Atiquzzaman
- 1992
(Show Context)
Citation Context ...ach level of approximation to the solution calculate the complete information of the parameter space in that level, and using those values make a decision. This is the case of the AHT 08) or the MHT. =-=(19)-=- Others only calculate a part of the parameter space in that level and decide, using this information, whether it is appropriate to continue investigating that subspace or maybe search in some otherJ ... |

17 |
Load Balancing Requirements in Parallel Implementations oflmage Feature Extraction Tasks
- Gerogiannis, Orphanoudakis
- 1993
(Show Context)
Citation Context ...tal vote over a subquadrant) we can choose a scatter (sparse cyclic) distribution of the points among the processors. ~3°) It will eventually be necessary to rebalance the load, as shown in reference =-=(31)-=-, when the new distribution compensates the overhead generated by rebalancing operation. We have studied different alternatives for dynamic balancing using distributed and centralized rebalancing mech... |

10 | Implementation and evaluation of Hough transform algorithms on a sharedmemory multiprocessor - Choudhary, Ponnusamy - 1991 |

9 | Circularity—a new principle underlying the design of accurate orientation operators - Davies - 1984 |

9 |
Dual Plane Variation of the Hough Transform for Detecting Non-Concentric
- Conker
- 1988
(Show Context)
Citation Context ...the noise points. 4. ELLIPSE DETECTION The points that make up an ellipse satisfy the following equation: [(xp - xo) cos ~ + (yp - Y0) sin ~b] 2 a 2 -+ [(xp - xo) sin ~b - (yp - Yo) cos ~b] 2 b2 = 1, =-=(9)-=- where Xo and Yo are the coordinates of the center, ~b is the orientation angle and a and b are the semiaxis. Using the traditional formulation of the FHT it is necessary to create a five-dimensional ... |

9 |
An ellipse detection method from the polar and pole definition of conics.
- Yoo, Sethi
- 1993
(Show Context)
Citation Context ...ey apply the Adaptive Hough Transform O8) in order to find the three remaining parameters. A higher uncoupling degree is achieved by Muammar and Nixon d4) who use three stages. Finally, Yoo and Seth° =-=(15)-=- find the possible parameters for each pair of points and after this, by means of a three stage process they extract the solutions. The algorithm for ellipse detection, Fast Ellipse Hough Transform (F... |

8 | Synchronous multiprocessor implementation of the Hough transform - Ben-Tzvi, Naqvi, et al. - 1990 |

5 |
Detection of an ellipse by use of a recursive leastsquare estimator
- Nagata, Tamura, et al.
- 1985
(Show Context)
Citation Context ...fies its value according to (3/ log2 N-3 min(j,t- 1) Cv = P ~ ~ 2 i. (4) j=0 i=0 So the final expression for the computational complexity is C = P[161og2N- 11] + [1 - 6(t)]2412t(log2 N - t) - logzN], =-=(5)-=- where 6(0 is 1 when t=0 and 1 for any other value of t. By choosing an adequate value for T, the number of computations can be significantly improved. A lower bound for this number will occur when t=... |

5 |
Elliptical feature extraction via an improved hough transform.
- Huang
- 1989
(Show Context)
Citation Context ...anOp. (12) b2 (Yp Yo) In the case where the ellipse is rotated an angle ~b this expression becomes: a 2 = (Xp - Xo) COS (~ -~- (yp -- YO) sin ~b tan(Op - (b). b 2 (x e - x0) sin ~b - (Ye - Y0) cos ~b =-=(13)-=- In this equation we know the values of the coordinates of the center of the ellipse from the application of the previous stage. Thus, we can use a two-dimensional space where each point of the ellips... |

4 |
Extracting elliptical figures from an edge vector field
- Tsukune, Goto
- 1983
(Show Context)
Citation Context ...g geometrical properties. After this and in order to obtain the five parameters of the ellipse, they apply the least squares method to the points that make up each of the candidates. Tsukune and Goto =-=(11)-=- perform the detection in three stages using information from the gradient vectors of the points of the image edge. Ho eta/. (16) use two stages. In the first one, two symmetrical axes (vertical and h... |

4 |
Tristage transform for multiple ellipse extraction
- Muammar, Nixon
- 1991
(Show Context)
Citation Context ...of the semiaxis ratio, we will call it h, in the equation of the ellipse so that the values of the semiaxis are given by: b = v/h -1 (Xp -- x0) 2 -- (yp -- yo) 2, a ---- V/(Xp - x0) 2 + h(yp - y0) 2. =-=(14)-=- It is necessary to point out that as a consequence of having obtained the semiaxis ratio in the previous stage we can reduce the complexity of the current one. This way, each point can carry out the ... |

3 |
A preprocessing method for Hough Transform to detect circles
- Ye
- 1996
(Show Context)
Citation Context ...nes again. middle of the lines rather than their parent quadrant. This way, for an image of size N × N, the total number of computations is given by expression: where Cc=P[161og2N- 11], C = C,. + Cv, =-=(2)-=- log 2 N 3 j / C~.=P 24 ~ Z2J "i=0 The first term, C,., indicates the number of computations carried out for all the quadrants that contain the solution. The expression for Cc is deduced taking into a... |

3 | New parallel Hough transform for circles
- Chan, Siu
- 1991
(Show Context)
Citation Context ...s ~21) and Chan eta/. (6) find the parameters of the circle employing two stages. In the first one they calculate the center and in the second the radius. In another more recent work by Chan and Siu, =-=(7)-=- the votes for thescenter and the radius are carried out in parallel using a double decomposition of the parameters in order to find the pairs x0 - Y0 and x0 - r simultaneously. In these algorithms, t... |

3 |
Bolle, The multiple window parameter transform
- Califano, M
- 1992
(Show Context)
Citation Context ... into the same window are going to be combined to calculate the parameters of the figures. The size of the windows is variable in order to adapt it to the different figures in the image. In the MWPT, =-=(23)-=- the size of the window is fixed but it is possible to combine the feature points from different windows to obtain the solutions. In the algorithm presented here, the abovementioned constraints guaran... |

3 | The Generalized Hough Transform on Mesh-Connected Computers - Ferreti - 1993 |

2 |
A new approach for efficient Hough transform for circles
- Chan, Siu
- 1989
(Show Context)
Citation Context ...r of active nodes per level. 3. CIRCLE DETECTION The geometrical place occupied by the points, P = (Xp~ yp), that make up the circumference of a circle is given by: (xp - xo) 2 -}- (yp - yo) 2 = r 2, =-=(6)-=- where Xo and Yo are the coordinates of the center and r is the radius of the circle. Applying the traditional HT we need a three-dimensional parameter space in order to accumulate the votations. This... |

2 | Parallel algorithms for circle detection - Kumar, Ranganathan, et al. - 1994 |

2 | A parallel pipelined hough transform - Guil, Zapata - 1996 |

2 | The Hough transform has O(N) complexity on NxN mesh connected computers - Cypher, Sanz, et al. - 1990 |

1 |
y F. Deravi, An efficient Method for Multiple-Circle Detection
- Cao
- 1990
(Show Context)
Citation Context ...ision of the quadrants introduced by the threshold T. If we choose T--P[2 t, the expression for C,, remains constant though Cv modifies its value according to (3/ log2 N-3 min(j,t- 1) Cv = P ~ ~ 2 i. =-=(4)-=- j=0 i=0 So the final expression for the computational complexity is C = P[161og2N- 11] + [1 - 6(t)]2412t(log2 N - t) - logzN], (5) where 6(0 is 1 when t=0 and 1 for any other value of t. By choosing ... |

1 |
A skimming technique for fast accurate edge detection, Signal Processing 26,116
- Davies
- 1992
(Show Context)
Citation Context ...der to avoid, as much as possible, the generation of erroneous solutions, we will use a technique that is analogous to the one employed in the case of linesJ z°~ That is, we will consider information =-=(8)-=- from the presence vector and we will eliminate the lines that have generated a center. 3.2. Detection of the radius Once the center of a circle is detected we can calculate its radius using the value... |

1 |
Fast segment Hough transform
- Guil, Villalba, et al.
- 1995
(Show Context)
Citation Context ...to choose a threshold value presents a problem; because if it is too small, many computations will be performed and if it is too large the solutions with less votes will not be detected. In reference =-=(20)-=- the problem is solved by executing the algorithm several times, starting with a large threshold value which is decreased in successive executions. The solutions extracted in one of the stages are eli... |

1 | Albanesi, Time complexity evaluation of algorithms for the Hough transform on mesh connected computers - Grazia - 1991 |

1 | The Hough transform has O(N) complexity on N x N mesh connected computers - Cypher, Sanz, et al. - 1990 |

1 |
Parallelization of irregular algorithms for shape detection
- Guil, Zapata
- 1996
(Show Context)
Citation Context ...he new distribution compensates the overhead generated by rebalancing operation. We have studied different alternatives for dynamic balancing using distributed and centralized rebalancing mechanisms. =-=(32)-=- Both mechanisms have a good behavior when the number of processors is low (less than 32), but it gets worse when this number is increased owing to the rebalancing mechanism overhead. The best results... |

1 | y W.C. Siu, A new approach for efficient Hough transform for circles - Chan - 1989 |

1 |
y W.C Siu, New parallel Hough transform for circles
- Chan
- 1991
(Show Context)
Citation Context ...nt a backmapping process in order to perform the labelling. This process has a computational Algorithm Computation Memory Conker [20] P��W 2 (1) N 2 Davies [10] Center N��P Radius f��P N 2=-= Chan y Siu [12] y-x Pairs N-=-��P x-r Pairs N��P N 2 FCHT Center P 2 /T Radius P P��log 2 N (1) WxW is the window size used to pairing points. Table V. Complexity of some Hough algorithms to detect circles. 20 complexi... |

1 | Parallel algortihms for circle detection - Kumar, Ranganathan, et al. - 1994 |

1 | A parallel Pipelined - Guil, Zapata - 1996 |