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Tag Archives: least squares
Gaze tracking as a novel input method
Smartphones and tablets usually have a camera on their back, to take photographs, and a frontal camera for videoconferencing. In a recent model (Samsung Galaxy S4) the frontal camera can be used as an input device too: … Continue reading
Posted in Uncategorized
Tagged computer vision, cone, digital camera, ellipse, eye, fitting, gaze tracking, iris, least squares, outlier, RANSAC, shape, smartphone, tablet
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Vanishing points in presence of noise
Most selfcalibration algorithms require a prior knowledge of the camera calibration matrix ; as an instance, you need it to normalize the image points as and therefore fit the essential matrix . With most commercial cameras it is safe to … Continue reading
Posted in Uncategorized
Tagged Alciatore and Miranda, calibration matrix, computer vision, constrained minimum, essential matrix, fitting, focal length, image of the absolute conic, Lagrange multipliers, lagrangian, least squares, noise, nonlinear regression, outlier, pixel pitch, principal point, RANSAC, vanishing point
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Orthogonal least squares fitting of a sphere/2
As said in my previous post, to obtain an orthogonal least squares fitting of a sphere to a cloud of points one should minimize the function Dave Eberly calls this the energy function, probably as a metaphorical reference to the … Continue reading
Orthogonal least squares fitting of a sphere
Recently I presented a linear method to obtain centre and radius of a sphere given four or more points on its surface, not all beginning to the same plane. This method is not completely satisfactory when working with more than … Continue reading
Linear least squares fitting of a circumference in 3D
In my last post I described how it is possible to find the centre and radius of a sphere given four or more points on its surface and not belonging to the same plane. What happens if the points do … Continue reading
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Tagged circumference, least squares, linear fitting, linear regression, sphere, SVD
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Linear least squares fitting of a sphere
The equation of a sphere with centre in and radius is or that is (1) with Writing (1) for four points on the sphere, , not belonging to the same plane, one gets a linear system of rank 4 in … Continue reading
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Tagged least squares, linear fitting, linear regression, sphere, SVD
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Constrained optimization without lagrangian multipliers
There is an obvious alternative to using lagrangian multipliers for constrained optimization: reformulate the problem in the subspace of constraints and it becomes automatically a non constrained problem. It is not always obvious, though, how one can do so in … Continue reading
Posted in Uncategorized
Tagged constraint subspace, least squares, optimization, plane, point, singular value decomposition, SVD
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