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

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Vanishing points in presence of noise

Most self-calibration 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

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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

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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

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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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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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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

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