Algorithm 1 Procedures of Contact Point Detection

Input data: foot points in the input depth image Output data: contact points Variables -$i$: index of the foot points in the depth image -$f_i$: i-th foot point in the depth image -$n_i$: normal vector of $f_i$ -$d_i$: distance from the footplate to $f_i$ -$c\_size$: length of one side of a cell in the 3D voxel grid Procedures: Constructing a 3D voxel grid: create a 3D voxel grid having a range of −1.0 to 1.0 and divide the grid into cells of equal size. Computing a normal vector: for all ${\mathrm{f}}_{\mathrm{i}}$, calculate the normal vector ${\mathrm{n}}_{\mathrm{i}}$ and apply a smoothing filter. Voting normal vectors: for all ${\mathrm{n}}_{\mathrm{i}}$, assign ${\mathrm{n}}_{\mathrm{i}}$ to the cell in the grid Setting initial clusters: set the non-empty cells as the initial clusters and calculate the average normal vector in the initial cluster. Merging adjacent clusters: for all inital clusters, calculate the distance between the adjacent cluster and merge them if the distance is smaller than $\mathrm{c}\_\mathrm{size}$. Estimating footplate equation: find the cluster with the largest number of normal vectors of the foot points and estimate the plane equation using the correspoindng foot points. Calculating distances of foot points: for all ${\mathrm{f}}_{\mathrm{i}}$, calculate the distance from the footplate using the plane equation. Constructing a histogram: create a hisgtorm of the distance from the foot points and the footplate. Detecting the contact points: find the bin with the highest frequency and define the points corresponding to the bin as the contact points.