Recent content by MarkoDe

I'll take a stab at simplifying. First, some notation: \widehat{c}_{i} is the row vector from the ith row of the matrix \widehat{C} = C^{-1} P_{p} is the 3x3 covariance matrix for the mean estimate p. P_{\alpha} is the 4x4 covariance matrix for the \alpha values. i,j are the row, column...

I'm interested in following your intuition, Stephen, but I don't quite understand. Wikipedia's definition for 'bilinear' didn't shed any light. Would you care to comment more?

Stephen, your interpretation looks correct to me. And I am indeed interested in quantities like VAR(\alpha_1) and COV(\alpha_1, \alpha_2) . Now that you guys have prodded me into formulating the question correctly, and you've interpreted it like that, the answer is beginning to be...

Hi Stephen and chiro. A point p in Cartesian coordinates can be expressed in barycentric coordinates as: p=\Sigma^{4}_{i=1}\alpha_{i}c_{i} where c_{i} is one of four control points, and \alpha is the weight for each control point. In this work, the following constraint is applied...

Thanks for your response, chiro. The mean is the output of triangulation algorithms, as described earlier. An example is available in the excellent computer vision book by Hartley and Zisserman, Multiple View Geometry: Multiple View Geometry on Google books The covariance is calculated...

Thanks for the replies, and for encouraging me to better define my query. What I have: I have an estimate of the location of a point in three dimensionsal space, which is expressed in Cartesian coordinates. The estimate was formed using sensors with some associated noise (in this case...

Hi folks, I know the covariance matrix and the location of a point, both of which are expressed in Cartesian coordinates. I am going to represent the point in barycentric coordinates, and I would like to represent the covariance matrix for the point in barycentric coordinates as well. Does...

Hi folks, I'm imagining the following situation: Two balls lie at the base of a hill, side by side, not touching. One is larger and masses more than the other. They are made from the same material. Suddenly, they both experience the same acceleration towards the hill. They don't ever come...