Apparatus, method and computer program for determining information about shape and/or location of an ellipse in a graphical image

• US 20080012860A1
• Filed: 04/03/2007
• Published: 01/17/2008
• Est. Priority Date: 09/30/2005
• Status: Active Grant

• Current Assignee: Fraunhofer Gesellschaft Zur Foerderung Der Angewandten Forsching E.V., Technische Universitã¤T Ilmenau
• Original Assignee: Fraunhofer Gesellschaft Zur Foerderung Der Angewandten Forsching E.V., Technische Universitã¤T Ilmenau
• Inventors: Katzmann, Johannes, Holland-Nell, Christian, Husar, Peter, Klefenz, Frank
• Granted Patent: US 7,948,493 B2
• Time in Patent Office: Days
• US Class Current: 345/441
• CPC Class Codes: G06T 7/64 of convexity or concavity
• CPC Class Codes: G06V 10/48 by mapping characteristic values of the pattern into a parameter space, e.g. Hough transformation
• CPC Class Codes: G06V 40/193 Preprocessing; Feature extraction

Abstract

An apparatus for determining information about shape and/or location of an ellipse includes a coordinate determination means for determining two coordinates of a first ellipse point representing a point of the ellipse located furthest in the first direction, and for determining two coordinates of a second ellipse point representing a point of the ellipse located furthest in a direction opposite to the first direction. The coordinate determination means is formed to determine at least parameters of a first bent line segment approximating the ellipse at the first ellipse point or in a surrounding of the first ellipse point, and to determine the coordinates of the first ellipse point based on the at least one parameter of the first bent line segment. Similarly, the coordinate determination means is formed to determine the coordinates of the second ellipse point. Furthermore, the inventive apparatus includes an ellipse calculation means for calculating at least one ellipse parameter of the ellipse based on the two coordinates of the first ellipse point and the two coordinates of the second ellipse point. The inventive apparatus here enables real-time-capable determination of parameters of an ellipse included in an image to be analyzed.

Claims

1. Apparatus (100;

800) for determining information (122) about shape and/or location of an ellipse in a graphical image (112;

812), the graphical image (112;

812) comprising a first direction (130;

x) and a second direction (132;

y), comprising;

a coordinate determination means (110;

400;

830, 832, 840, 842) for determining two coordinates (x₁′

, y₁′

;

x₃, y₃) of a first ellipse point (136;

226) representing a point of the ellipse (134;

220) located furthest in the first direction (130;

x), and

for determining two coordinates (x₃′

, y₃′

;

x₁, y₁) of a second ellipse point (138;

228) representing a point of the ellipse (134;

220) located furthest in a direction opposite to the first direction (130;

x),

wherein the coordinate determination means (110;

420;

430;

814, 830, 832, 840, 842) is formed to determine at least one parameter of a first bent line segment (146) approximating the ellipse (134;

220) at the first ellipse point (136;

226) or in a surrounding of the first ellipse point (136;

226), and to determine the coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point (136;

226) based on the at least one parameter of the first bent line segment (146), and

to determine at least one parameter of a second bent line segment (148) approximating the ellipse (134;

220) at the second ellipse point (138;

228) or in a surrounding of the second ellipse point (138;

228), and to determine the coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point (138;

228) based on the at least one parameter of the second bent line segment (148); and

an ellipse calculation means (120;

850) for calculating at least one ellipse parameter (x_m′

, x_m′

, a′

, b′

, α

′

;

x_m, y_m, a, b, α

) based on the two coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point (136;

226) and the two coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point (138;

228),

wherein the at least one ellipse parameter (x_m′

, y_m′

, a′

, b′

, α

′

;

x_m, y_m, a, b, α

) represents the information (122) about the shape and/or the location of the ellipse (134;

220).

2. Apparatus (100;

800) according to claim 1,

wherein the coordinate determination means (110;

400;

814, 830, 832, 840, 842) further is formed to determine at least one coordinate (x₄′

, y₄′

;

x₂, y₂) of a third ellipse point (140;

230) representing a point of the ellipse (134;

220) located furthest in the second direction (132;

y),

wherein the coordinate determination means (110;

400;

814, 830, 832, 840, 842) is formed to determine at least one parameter of a third bent line segment (150) approximating the ellipse (134;

220) at the third ellipse point (140;

230) or in a surrounding of the third ellipse point (140;

230), and

to determine at least one coordinate (x₄′

, y₄′

;

x₂, y₂) of the third ellipse point (140;

230) based on the at least one parameter of the third bent line segment (150),

wherein the ellipse calculation means (110) is formed to calculate at least one ellipse parameter (x_m′

, y_m′

, a′

, b′

, α

′

;

x_m, y_m, a, b, α

) based on the two coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point (136;

226), the two coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point (138;

228) and the at least one coordinate (x₄′

, y₄′

;

x₂, y₂) of the third ellipse point (140;

230).

3. Apparatus (100;

800) according to claim 1 or 2, wherein the graphical image (112;

812) is a raster image (310) including a plurality of image points (312, 314) arranged in a plurality of raster rows (320, 330, 332, 334, 368, 372) and/or in a plurality of raster columns (322, 336, 338, 340, 362, 366), wherein the ellipse (134, 220;

350) is described by a plurality of image points forming ellipse points, and/or wherein the first bent line segment (146) can be described by a plurality of adjacent image points, and/or wherein the second bent line segment (148) can be described by a plurality of adjacent image points, and/or wherein the third bent line segment (150) can be described by a plurality of adjacent image points.

4. Apparatus (100;

800) according to claim 3, wherein the coordinate determination means (110;

400;

814, 830, 832, 840, 842) is formed to perform a pattern recognition, using the raster rows (320, 330, 332, 334, 368, 372) and/or the raster columns (322, 336, 338, 340, 362, 366), in order to identify, in an image excerpt (360, 364, 370, 374, 380;

740;

1320, 1330) of the image to be identified, which is formed by a plurality (360;

364;

370;

374;

380) of raster rows and/or raster columns, a curve course (510, 520, 560, 570) forming the first bent line segment (146), and to determine at least one parameter of the identified curve course (510, 520, 560, 570) as a parameter of the first bent line segment (146).

5. Apparatus (100;

800) according to claim 4, wherein the coordinate determination means (110;

400;

814, 830, 832, 840, 842) is formed to perform a pattern recognition, using the raster rows (320, 330, 332, 334, 368, 372) and/or raster columns (322, 336, 338, 340, 362, 366), in order to identify, in the image excerpt (1320, 1330) of the image (112;

310;

812;

1300) to be identified, which is formed by the plurality (360, 364, 370, 374, 380) of raster rows and/or raster columns, a curve course forming the first bent line segment (146), by checking if the image excerpt (1320, 1330) to be analyzed includes a curve course that is sufficiently similar to a reference curve course from a first set of possible reference curve courses (452, 454, 456) with respect to a given similarity measure, wherein the first set of possible reference curve courses (452, 454, 456) describes admissible courses of the first bent line segment (146) for various parameters of the first bent line segment (146),

and/or to identify, in the image excerpt (1320, 1330) of the image (112;

310;

812;

1300) to be analyzed, which is formed by the plurality (360, 364, 370, 374, 380) of raster rows (320, 330, 332, 334, 368, 372) and/or raster columns (322, 336, 338, 340, 362, 366), a curve course forming the second bent line segment (148), by checking if the image excerpt (1320, 1330) to be analyzed includes a curve course sufficiently similar to a reference curve course from a second set of possible reference curve courses (452, 454, 456) with reference to a given similarity measure, wherein the second set of possible reference curve courses (452, 454, 456) describes admissible courses of the second bent line segment (148) for various parameters of the second bent line segment (148),

and/or to identify, in the image excerpt (1320, 1330) of the image (112;

310;

812;

1300) to be analyzed, which is formed by the plurality (360, 364, 370, 374, 380) of raster rows (320, 330, 332, 334, 368, 372) and/or raster columns (322, 336, 338, 340, 362, 366), a curve course forming the third bent line segment (150), by checking if the image excerpt (1320, 1330) to be analyzed includes a curve course sufficiently similar to a reference curve course from a third set of possible reference curve courses with reference to a given similarity measure, wherein the third set of possible reference curve courses describes admissible courses of the third bent line segment (150) for various parameters of the third bent line segment (150).

6. Apparatus (100;

800) according to claim 5, wherein the set of possible reference curve courses (452, 454, 456) describes curve courses differing with reference to their location and/or shape, wherein at least one parameter characterizing the location and/or shape is associated with a curve course from the plurality of possible reference curve courses (452, 454, 456), and wherein the coordinate determination means (110;

400;

814, 830, 832, 840, 842) is formed to derive the parameter of the first bent line segment (146) approximating the ellipse (134) at the first ellipse point (136), the parameter of the second bent line segment (148) approximating the ellipse at the second ellipse point (138), or the parameter of the third bent line segment (150) approximating the ellipse at the third ellipse point (140), from the fact as to which one of the curve courses from the plurality of possible reference curve courses (452, 454, 456) is sufficiently similar to a curve course in the image excerpt (1320, 1330) with reference to the given similarity measure.

7. Apparatus (100;

800) according to claim 5 or 6, wherein the curve courses are chosen from the plurality of possible reference curve courses (452, 454, 456) so that they approximate ellipses of different shape and/or location at the first ellipse point or at the second ellipse point or at the third ellipse point.

8. Apparatus (100;

800) according to one of claims 5 to 7, wherein the curve courses are selected from the plurality of possible reference curve courses (452, 454, 456) so that they describe excerpts from circular curves of different location and/or different radius.

9. Apparatus (100;

800) according to one of claims 1 to 8, wherein the coordinate determination means (110;

400;

814, 830, 832, 840, 842) is formed to apply a pattern recognition (420;

830, 832, 840, 842) to a plurality of image excerpts (360, 364, 370, 374, 380;

740;

1320, 1330) of the image (112;

310;

812;

1300) to be analyzed, in order to identify, in the plurality of image excerpts (360, 364, 370, 374, 380;

740;

1320, 1330) to be analyzed, a curve course forming the first bent line segment (136), and to determine a location parameter of the first bent line segment (136), based on in which one of the plurality of image excerpts (360, 364, 370, 374, 380;

740;

1320, 1330) of the image (112;

310;

812;

1300) the first bent line segment (136) is identified.

10. Apparatus (100;

800) according to claim 9, wherein the coordinate determination means (110;

400;

814, 830, 832, 840, 842) is formed to apply the pattern recognition (400;

830;

832;

840;

842) to the plurality of image excerpts (360, 364, 370, 374, 380;

740;

1320, 1330) of the image (112;

310;

812;

1300) to be analyzed, wherein the image excerpts to be analyzed are chosen so that at least two image excerpts of the plurality of image excerpts (360, 364, 370, 374, 380;

740;

1320, 1330) to be analyzed overlap.

11. Apparatus (100;

800) according to one of claims 1 to 10, wherein the coordinate determination means (110;

400;

814, 830, 832, 840, 842) is formed to determine at least a further coordinate (x₄′

, y₄′

;

x₂, y₂) of the third ellipse point (140;

230) as an additional coordinate, or at least one coordinate (x₂′

, y₂′

;

x₀, y₀) of a fourth ellipse point (142;

232) representing a point of the ellipse (132;

220) located furthest in a direction opposite to the second direction (132;

y),

wherein the ellipse calculation means (120;

850) is formed to calculate a first set of ellipse parameters including at least one ellipse parameter, based on the two coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point (136;

226), the two coordinates (x₃′

, y₃′

;

x₁, y₁) of the third ellipse point (138;

228) and the first coordinate (x₄′

, y₄′

;

x₂, y₂) of the third ellipse point (140;

230), as well as to calculate a second set of ellipse parameters including at least one ellipse parameter, based on the two coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point (136;

226), the two coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point (138;

228) and the additional coordinate (x₄′

, y₄′

, x₂′

, y₂′

;

x₀, y₀, x₂, y₂), and to calculate a result set of ellipse parameters (x_m′

, y_m′

, a′

, b′

, α

′

;

x_m, y_m, a, b, α

) by averaging, using the first set of ellipse parameters and the second set of ellipse parameters.

12. Apparatus (100;

800) according to one of claims 1 to 11, wherein the coordinate calculation means (110;

400;

814, 830, 832, 840, 842) is formed to determine two coordinates (x₄′

, y₄′

;

x₂, y₂) of the third ellipse point (140;

230) representing a point of the ellipse located furthest in the second direction (132;

y), and two coordinates (x₂′

, y₂′

;

x₀, y₀) of a fourth ellipse point (142;

232) representing a point of the ellipse located furthest in a direction opposite to the second direction (132;

y), and further to select a plurality of different sets of three ellipse points from the first ellipse point (136;

226), the second ellipse point (138;

228), the third ellipse point (140;

230) and the fourth ellipse point (142;

232), in order to determine associated sets of ellipse parameters (x_m′

, y_m′

, a′

, b′

, α

′

;

x_m, y_m, a, b, α

) for the sets of ellipse points (136, 138, 140, 142;

226, 228230, 232), and to calculate an average set of ellipse parameters as information about the shape and/or the location of the ellipse (134;

220) by averaging of the sets of ellipse parameters belonging to the sets of ellipse points.

13. Apparatus according to one of claims 1 to 12, wherein the coordinate determination means (110;

400;

814, 830, 832, 840, 842) is formed to determine two coordinates (x₄′

, y₄′

;

x₂, y₂) of the third ellipse point (140;

230) representing a point of the ellipse (134;

220) located furthest in the second direction (132;

y), and

wherein the ellipse calculation means (120;

850) is further formed to calculate center coordinates (x_m, y_m) of the ellipse (134;

220) from the two coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point (136;

226) and the two coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point (138;

228),

to perform a coordinate transform of the coordinates (x₁′

, y₁′

, x₄′

, y₄′

;

x₃, y₃, x₂, y₂) of the first ellipse point (136;

226) and of the third ellipse point (140;

230), in order to obtain transformed coordinates (x_x, y_x, x_y, y_y) of the first ellipse point (136;

226) and the third ellipse point (138;

228), wherein the coordinate transform is formed to shift a center (240) of the ellipse (134;

220) described by the center coordinates (x_m, y_m) into a coordinate origin (264),

to calculate an estimated transformed second coordinate y_y,calc of the third ellipse point, using the determination equation

$1=\frac{y_{y,\mathrm{calc}}·<br><br>x_y}{y_x·<br><br>x_x}<br><br>5$

wherein x_x is the transformed first coordinate of the first ellipse point (136;

226), wherein y_x is the transformed second coordinate of the first ellipse point (136;

226), and wherein x_y is the transformed first coordinate of the third ellipse point (140;

230),

and to decide if the third ellipse point (140;

230) belongs to the ellipse (134;

220) described by the first ellipse point (136;

226) and the second ellipse point (138;

228), based on a deviation between the estimated transformed second coordinate y_y,calc of the third ellipse point (140;

230) and the transformed second coordinate y_y of the third ellipse point (140;

230) determined by the coordinate transform.

14. Apparatus (100;

800) according to one of claims 1 to 13,

wherein the ellipse calculation means (120;

850) is formed to calculate a first center coordinate x_m of the ellipse (134;

220), based on the first coordinate x₃ of the first ellipse point (226) and the first coordinate x₁ of the second ellipse point (228), using the calculation rule

$x_m=\frac{x_3+x_1}{2},$

and/or to calculate a second center coordinate y_m of the ellipse (134;

220), based on the second coordinate y₃ of the first ellipse point (226) and the second coordinate y₁ of the second ellipse point (228), using the calculation rule

$y_m=\frac{y_3+y_1}{2}<br><br>.5$

15. Apparatus (100;

800) according to claim 14, wherein the ellipse calculation means (120;

850) is further formed to calculate a rotational angle α

of the ellipse (134;

220), a length a of a first semiaxis of the ellipse (134;

220) and/or a length b of a second semiaxis of the ellipse (134;

220), using the following determination equations;

16. Apparatus (100;

800) according to one of claims 1 to 15, wherein the coordinate determination means (110;

400;

814, 830, 832, 840, 842) comprises a pattern recognition means (420;

600;

830, 832, 840, 842), which is formed to receive a plurality of raster rows (320, 330, 332, 334, 368, 372) to be analyzed or of raster columns (322, 336, 338, 340, 362, 366) to be analyzed in form of a plurality of parallel time signals (612, 614, 616), and to forward the time signals (612, 614, 616) at different speeds in parallel through a plurality of stages (610) connected one behind the other,

wherein at least one predetermined stage (610) includes a summing means (630), which is formed to sum signals coming out of the predetermined stage (610), in order to form a column sum (632), and

wherein the pattern recognition means (600) is further formed to evaluate the column sum (632), in order to determine information about a bent line segment (146, 148, 150, 152) included in the raster rows (320, 330, 332, 334, 368, 372) or raster columns (322, 336, 338, 340, 362, 366) received from the pattern recognition means (600),

wherein the information includes at least one parameter of the bent line segment (146, 148, 150, 152) included in the received raster rows (320, 330, 332, 334, 368, 372) or raster columns (322, 336, 338, 340, 362, 366).

17. Apparatus (100;

800) according to claim 16, wherein the predetermined stage (610) further comprises a threshold value recognition means (634), which is formed to receive and recognize the column sum (632) if at least a predetermined number of signals (612, 614, 616) at the output of the predetermined stage (610) are active at the same time,

wherein the pattern recognition means (420;

600;

830, 832, 840, 842) is further formed to evaluate an output signal of the threshold value recognition means (634), in order to determine at least one parameter of a bent line segment (146, 148, 150, 152) included in the received raster rows (320, 330, 332, 334, 368, 372) or raster columns (322, 336, 338, 340, 362, 366).

18. Apparatus (100;

800) according to claim 16 or 17, wherein the pattern recognition means (420;

600;

830, 832, 840, 842) is formed to distort a curved curve course (1410), which is described by the signals (612, 614, 616;

1510) received by the pattern recognition means (420;

600;

830, 832, 840, 842), step by step when passing through the stages (610;

1530) connected one behind the other, due to the differently fast propagation of the signals (612, 614, 616;

1510), in order to obtain a distorted description (1420, 1430, 1440) of the curved curve course, and to recognize if an approximately straight line (1450) represented by a plurality of concurrently active signals (612, 614, 616;

1510) in a particular stage (610) is described by the distorted description.

19. Apparatus (100;

800) according to one of claims 16 to 18, wherein the at least one stage (610;

1530) of the pattern recognition means (420;

600;

830, 832, 840, 842) is formed to delay several signals (612, 614, 616;

1510) in differently strong manner when forwarding same through the stage (610;

1530).

20. Apparatus (100;

800) according to one of claims 16 to 19, wherein the pattern recognition means (420;

600;

830, 832, 840, 842), by establishing different delays (620, 624) when forwarding the signals (612, 614, 616) through the stages (610), is formed so that a circularly bent line segment included in the raster rows (320, 330, 332, 334, 368, 372) or raster columns (322, 336, 338, 340, 362, 366) received by the pattern recognition means is deformed approximately to a straight line after passing through a number of stages (610;

1530),

wherein the pattern recognition means (420;

600;

830, 832, 840, 842) is formed to recognize presence of an approximately straight line and to determine after passing through how many stages the straight line is present, and

wherein the pattern recognition means (420;

600;

830, 832, 840, 842) is further formed to derive at least one parameter of the circularly bent line segment received by the pattern recognition means from the number of stages passed through until the presence of an approximately straight line.

21. Apparatus (100;

800) according to one of claims 10 to 20, wherein the pattern recognition means (420;

600;

830, 832, 840, 842), by establishing different delays (620, 624) when forwarding the signals (612, 614, 616) through the stages (610), is formed so that a circularly bent line segment included in the raster rows (320, 330, 332, 334, 368, 372) or raster columns (322, 336, 338, 340, 362, 366) received by the pattern recognition means (420;

600;

830, 832, 840, 842) is deformed approximately to a straight line after passing through a number of stages, wherein the pattern recognition means is formed to recognize presence of an approximately straight line and to derive at least one parameter of the circularly bent line segment received by the pattern recognition means, based on the time instant at which the approximately straight line is present.

22. Apparatus (100;

800) according to one of claims 10 to 21, wherein the coordinate determination means (110;

412, 420, 430;

840, 820, 822, 830, 832) is formed to supply the image (112;

310;

812) to the pattern recognition means (420;

600;

820, 822, 830, 832) twice in form of successively transmitted raster rows (320, 330, 332, 334, 368, 372) to be analyzed,

wherein the coordinate determination means is further formed to supply the image to the pattern recognition means for a determination of the two coordinates (x₃, y₃) of the first ellipse point (226), beginning with a raster row (320) of the image located at a first edge of the image, and to supply the image to the pattern recognition means for a determination of the two coordinates (x₁, y₁) of the second ellipse point (228), beginning with a raster row (334) of the image located at a second edge of the image, wherein the first edge of the image is opposite to the second edge of the image, and wherein the pattern recognition means is formed to recognize bent line segments with a given direction of curvature.

23. Apparatus (100;

800) according to one of claims 10 to 22, wherein the coordinate determination means (110;

420;

814, 820, 822, 830, 832) includes a first pattern recognition means (830) and a second pattern recognition means (832), wherein the first pattern recognition means (830) is formed to recognize bent line segments with a first given direction of curvature, wherein the second pattern recognition means (832) is formed to recognize bent line segments with a second direction of curvature opposite to the given first direction of curvature, and wherein the coordinate determination means is formed to supply the image to the first pattern recognition means (830) for a determination of the two coordinates (x₃, y₃) of the first ellipse point (226), beginning with a raster row (320) located at a first edge of the image, and to provide the image to the second pattern recognition means (832) for a determination of the two coordinates (x₁, y₁) of the second ellipse point (228), beginning with a raster row (320) located at the first edge of the image.

24. Apparatus (100;

800) according to one of claims 10 to 23, wherein the pattern recognition means (412, 420;

600) is formed to process a first plurality (370) of raster rows to be analyzed as well as a second plurality (374) of raster rows to be analyzed, wherein the first plurality of raster rows to be analyzed and the second plurality of raster rows to be analyzed overlap, and

wherein the pattern recognition means (420) is further formed to determine a location parameter of the curve course to be identified based on whether the curve course (146, 148, 150, 152) to be identified is identified in an analysis of the first plurality of raster rows to be analyzed or in an analysis of the second plurality of raster rows to be analyzed.

25. Apparatus (100;

800) according to one of claims 1 to 24, wherein the first direction (130;

x) is orthogonal to the second direction (132;

y).

26. Apparatus (100;

800) according to one of claims 1 to 25, wherein the apparatus for determining information about the shape and/or the location of an ellipse is formed to receive a binary edge image (310) as graphical image (112;

812), wherein the binary edge image describes at least one edge by at least one line (350) in form of active image points (312), whereas locations in the edge image at which no edge is present are described by non-active image points (314).

27. Apparatus (100;

800) according to one of claims 1 to 26, wherein the apparatus is further formed to derive the graphical image (112;

812) from video data from a video data source.

28. Apparatus (100;

800) according to one of claims 1 to 27, further comprising a data interface or a display device, which is formed to output the information about the shape and/or the location of the ellipse to an electrical processing means or a human user.

29. Apparatus (100;

800) according to one of claims 1 to 28, wherein the apparatus for determining information about the shape and/or the location of an ellipse is formed to preprocess the graphical image (112;

812) by a threshold value binarization, in which a light value or a dark value is associated with each image point of the graphical image, depending on the result of a comparison of a color value and/or a brightness value with a threshold value, in order to obtain a binarized image,

and further to apply edge detection to the binarized image, wherein the edge detection is formed to generate an edge image from the binarized image, in which edge-shaped transitions from the light value to the dark value in the binarized image are characterized as a line-shaped edge,

wherein the coordinate determination means is further formed to process the edge image.

30. Apparatus (100;

800) according to one of claims 1 to 29, wherein the apparatus is further formed to obtain the graphical image from a video camera arranged to capture a pupil of a human eye,

and wherein the apparatus further includes a data interface formed to transmit the information about the shape and/or the location of the ellipse to an apparatus for calculating a viewing direction of the human eye.

31. Apparatus (100;

800) according to one of claims 1 to 30, wherein the apparatus further includes an interface formed to output the information about the shape and/or the location of the ellipse to a mechanical positioning means formed to cause mechanical motion, depending on the information about the shape and/or the location of the ellipse.

32. Method (1700) for determining information (122;

1780) about shape and/or location of an ellipse (134;

220) in a graphical image (112;

812;

1710), the image (112;

812;

1710) comprising a first direction (130;

x) and a second direction (132;

y), comprising the steps of;

determining (1720) two coordinates (x₁′

, y₁′

;

x₃, y₃) of a first ellipse point (136;

226) representing a point of the ellipse (134;

220) located furthest in the first direction (130;

x),

determining (1730) two coordinates (x₃′

, y₃′

;

x₁, y₁) of a second ellipse point (138;

228) representing a point of the ellipse (134;

220) located furthest in a direction opposite to the first direction (130;

x),

wherein determining (1720) the two coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point (136;

226) includes determining at least one parameter of a first bent line segment (146) approximating the ellipse at the first ellipse point or in a surrounding of the first ellipse point, as well as determining the coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point (136;

226), based on the at least one parameter of the first bent line segment (146), and

wherein determining (1730) the two coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point (138;

228) includes determining at least one parameter of a second bent line segment (148) approximating the ellipse at the second ellipse point (138;

228) or in a surrounding of the second ellipse point (138;

228), as well as determining the coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point (138;

228), based on the at least one parameter of the second bent line segment (148); and

calculating (1740) at least one ellipse parameter (x_m, y_m) of the ellipse, based on the two coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point and the two coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point,

wherein the at least one ellipse parameter (x_m, y_m) represents information about the shape and/or the location of the ellipse.

34. Computer program for performing the method according to claim 32 or 33, when the computer program is executed on a computer.

33. Method (1700) for determining information (122;

1780) about shape and/or location of an ellipse (134;

220) in a graphical image (112;

812;

1710), the image (112;

812;

1710) comprising a first direction (130;

x) and a second direction (132;

y), comprising the steps of;

determining (1720) two coordinates (x₁′

, y₁′

;

x₃, y₃) of a first ellipse point (136;

226) representing a point of the ellipse (134;

220) located furthest in the first direction (130;

x),

determining (1730) two coordinates (x₃′

, y₃′

;

x₁, y₁) of a second ellipse point (138;

228) representing a point of the ellipse (134;

220) located furthest in a direction opposite to the first direction (130;

x),

wherein determining (1720) the two coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point (136;

226) includes identifying a first bent line segment approximating the ellipse at the first ellipse point or in a surrounding of the first ellipse point, determining at least one parameter of the identified first bent line segment (146), as well as determining the coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point (136;

226), based on the at least one parameter of the identified first bent line segment (146), and

wherein determining (1730) the two coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point (138;

228) includes identifying a second bent line segment approximating the ellipse at the second ellipse point (138;

228) or in a surrounding of the second ellipse point (138;

228), determining at least one parameter of the identified second bent line segment (148), as well as determining the coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point (138;

228), based on the at least one parameter of the identified second bent line segment (148), and

calculating (1740) at least one ellipse parameter (x_m, y_m) of the ellipse, based on the two coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point and the two coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point,

wherein the at least one ellipse parameter (x_m, y_m) represents information about the shape and/or the location of the ellipse.

35. Apparatus (100;

800) for determining information (122) about shape and/or location of an ellipse in a graphical image (112;

812), the graphical image (112;

812) comprising a first direction (130;

x) and a second direction (132;

y), comprising;

a coordinate determination means (110;

400;

830, 832, 840, 842) for determining two coordinates (x₁′

, y₁′

;

x₃, y₃) of a first ellipse point (136;

226) representing a point of the ellipse (134;

220) located furthest in the first direction (130;

x), and

for determining two coordinates (x₃′

, y₃′

;

x₁, y₁) of a second ellipse point (138;

228) representing a point of the ellipse (134;

220) located furthest in a direction opposite to the first direction (130;

x),

wherein the coordinate determination means (110;

420;

430;

814, 830, 832, 840, 842) is formed to identify a first bent line segment approximating the ellipse (134;

220) at the first ellipse point (136;

226) or in a surrounding of the first ellipse point (136;

226), to determine at least one parameter of the identified first bent line segment (146), and to determine the coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point (136;

226), based on the at least one parameter of the identified first bent line segment (146), and

to identify at least one second bent line segment approximating the ellipse (134;

220) at the second ellipse point (138;

228) or in a surrounding of the second ellipse point (138;

228), to determine at least one parameter of the identified second bent line segment (148), and to determine the coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point (138;

228), based on the at least one parameter of the identified second bent line segment (148), and

an ellipse calculation means (120;

850) for calculating at least one ellipse parameter (x_m′

, x_m′

, a′

, b′

, α

′

;

x_m, y_m, a, b, α

), based on the two coordinates (x₁′

, y₁′

;

x₃, y₃) of the first ellipse point (136;

226) and the two coordinates (x₃′

, y₃′

;

x₁, y₁) of the second ellipse point (138;

228),

wherein the at least one ellipse parameter (x_m′

, y_m′

, a′

, b′

, α

′

;

x_m, y_m, a, b, α

) represents the information (122) about the shape and/or the location of the ellipse (134;

220).