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..., (24) 7where C10 and C20 can be computed from the detected ellipses. The distance between the two circle centers (d12) can be calculated by the following expression, d12 = |C1 −C2| = |z0||C10 −C20|. =-=(25)-=- A world coordinate system O-XY Z can be defined by using the two circle centers as reference points and the unit normal vector of the supporting plane as a reference direction as following. Let C1 be...

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... a series of individual pressure values, but as a series of "blobs" of pressure centred at particular points. Existing algorithms for fitting ellipses to sets of points, such as least squares fitting =-=[3,5]-=-, are very computationally intensive and so are problematic for implementation on embedded hardware. We intend to investigate simpler, but less robust methods to match blobs, and then evaluate their s...

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...ates of bu AML of some sort) and ellipse-specific estimates obtainable with use of an improved version of the direct least-squares fitting algorithm of Fitzgibbon et al. [3], due to Halír and Flusser =-=[15]-=-. Fig. 4. Performance histograms for each of the methods, with JAML bins on the x-axes, and frequencies of occurrence on the y-axes. ability distributions for zðx1Þ; ...;zðxnÞ, with the random variabl...

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...by the intersection of two 3-D elliptical cones. b) The model is found by intersecting the 3-D elliptical cone with the plane determined by the 2-D line and the optical center. 396 A. Brost et al. in =-=[7]-=-. Specifically, the method uses a least square estimation of the ellipse parameters f = (a, b, c, d, e, f)T of the ellipse equation au2+buv+cv2+du+ev+f = 0 with the 2-D coordinates u and v. Given a se...

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... 0 z0 ]T = R cx (5) M = R M (6) Nij = Mij M3 j α0, i = {1, 2, 3} j = {1 . . . n} (7) The x and y coordinates of the j normalized contour points (Eq. 7) represent the intersections of cx j with a plane normal to cx through c (0, 0, α0) (Eq. 8). Therefore we introduce the coordinate system of the ellipse plane denoted e with origin in c (0, 0, α0). e p j i = Nij, i = {1, 2} j = {1 . . . n} (8) The e p j describe an ellipse which is defined by an implicit second order polynomial (Eq. 9). The polynomial coefficients are found by applying a numerically stable direct least squares fitting method [18] on F (x, y) = ax2 + b xy + cy2 + dx + ey + f = 0 (9) with an ellipse specific constraint b 2 − 4ac < 0. J Intell Robot Syst The a, b , c, d, e, f are the ellipse parameters and e (x, y) are the coordinate points obtained by the normalization procedure above. The result of the least squares fitting are two vectors a1 = ⎛ ⎝ a b c ⎞ ⎠ , a2 = ⎛ ⎝ d e f ⎞ ⎠ containing the parameters which satisifes the least squares condition. The conic section equation (Eq. 9) can be transformed with the substitution x = u cos φ − v sin φ y = u sin φ + v cos φ and the well known definition tan 2φ = b a − c into a...

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...moving from the base color away from the copunctal point, resulting in six differentiation limits. These six limits are then used to generate the best-fit ellipse using approaches outlined in [7] and =-=[9]-=-. The half lengths of the major and minor axes of this best-fit ellipse are then used to find the ellipsoid. Figure 3. Confusion line colors for individuals with tritanopia (blue-yellow dichromatic CV...

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...as explained in [16]. This step provides the points pi =(ui,vi) T with i =1,...,N of the catheter device. The 2-D ellipses are then calculated such that all ellipse points satisfy the linear equation =-=[17]-=- au 2 i + buivi + cv 2 i + dui + evi + f =0 (1)3 with the 2-D coordinates u and v. Thepointspiof the catheter are combined in a measurement matrix [18] ⎛ u M = ⎜ ⎝ 2 1 u1v1 v2 1 u1 v1 1 . . . . . . u...

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...termines all other possible hue scalings. In testing this conjecture, we will use as reference surface the centroid of all of the surface patches under a single light. We do not assume that this surface, which the subject never sees, is precisely achromatic, but, given the construction of our stimuli, it will be nearly so. We tested the Speigle–Brainard conjecture in the following way. First, we transformed all opponent data of subject i to u¶v¶ using the specific transformation that was given by Mi and ci. Then, we fitted optimal ellipses to the u¶v¶ data of each subject for each illuminant (Halir & Flusser, 1998). Finally, we compared the parameters of the ellipse for neutral illumination data with those of the ellipses for the chromatic illumination data. Analyzing the parameters of the ellipses is advantageous in that we can directly separate effects of color constancy from deviations from the Speigle–Brainard conjecture. If we analyze the ellipses for neutral and chromatic illumination, then differences in the centroids reflect incomplete color constancy. However, differences in area, eccentricity (shape), or orientation of the ellipses indicate deviations from the Speigle–Brainard conjecture. If t...

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... distance, the more dissimilar the nodule and the ellipsoid are. The usual techniques to estimate the ellipse location in an image are based on the Hough transform or the principal axis estimation [7]=-=[8]-=-. We propose an algorithm to estimate, in a very accurate way, the ellipse location in an image by minimizing the mean distance from a set of points to the ellipse. This minimization criterion has a m...