User:DrSammo

Learning joint vote weights
Need to minimise this:

$$\int (x - \hat{x})^2 p(x) dx$$

where $$x$$ is the predicted joint location, $$\hat{x}$$ is the ground truth joint location and:

$$p(x) = {{p(\hat{x} = x | I)}\over{\int p(\hat{x} = x | I)dx}}$$

where I is the training image.

For implementation I need to minimise the following:

$$\sum_{i=1}^{N_i} \sum_{j=1}^{N_j} \sum_{p=1}^{N_p} {{\sum_{c=1}^{N_c} \delta_{pc} [(x_p + V_{cj}) - \hat{x}_{ij}]^2 W_{cj}}\over{\sum_{c=1}^{N_c} \delta_{pc} W_c}}$$

Where $$N_i$$ is the number of training images, $$N_p$$ is the number of patches/features found in each image, $$N_c$$ is the number of patches in the codebook (set of known patches/features learnt earlier from training data), $$\delta_{pc}$$ is 1 if the image patch $$p$$ matches the codebook patch $$c$$ and 0 otherwise, $$x_p$$ is the patch location in the training image, $$V_c$$ is the vector to the predicted joint location, and $$W_c$$ is the weight, or confidence that this patch has about the joint location being at $$X_p + V_c$$.