# jrmpc Joint registration of multiple point sets See: G. D. Evangelidis, D. Kounades-Bastian, R. Horaud, andE. Z. Psarakis. A generative model for the joint registration of multiple point sets. In European Conference on Computer Vision, pages 109–122. Springer, 2014 ```r jrmpc( V, C = NULL, K = NULL, g = NULL, initialPriors = NULL, updatePriors = TRUE, maxIter = 100, fixedVarIter = 0, tol = 0.01, initializeBy = NULL, model.selection = FALSE, model.selection.threshold = NULL, rotation.only = FALSE ) ``` ## Arguments - `V`: list of point sets as N x D matrices - `C`: (optional) list of arrays of covariance matrices with C[[j]][,,i] the covariance matrix associated with point i of set j. - `K`: (optional) number of components of the GMM, defaults to the average number of points in a set. - `g`: (optional) proportion of noisy points, defaults to 1/K. If set, priors will be initialized uniformly. - `initialPriors`: (optional) vector of length K of prior probabilities. Defaults to uniform distribution using g. If set, will determine g so it is an error to specify g with initialPriors. - `updatePriors`: logical, whether to update priors at each iteration (default: TRUE). - `maxIter`: maximum number of iterations to perform (default: 100). - `fixedVarIter`: number of iterations before starting variance updates - `tol`: tolerance for determining convergence (default: 1e-2). - `initializeBy`: (optional) how to initialize the GMM means. Defaults to distributing the means on the surface of the sphere enclosing all (centred) sets. Currently supported values are: * 'sampling': sample from the data, * a K x D matrix of points - `model.selection`: whether to perform model selection (default: FALSE). If set to TRUE, GMM components with no support in the data are deleted. - `model.selection.threshold`: value below which we consider a GMM component has no support, set to 1/K if not explicitly given - `rotation.only`: if set to TRUE, no translation is performed (default: FALSE) ## Returns a list of * Y: list of transformed point sets as N x d matrices, * R: list of d x d rotation matrices, one for each point set in V, * t: list of translation vectors, one for each point set in V, * M: centres of the GMM, * S: variances of the GMM. * a: list of posterior probabilities as N x K matrices * iter: number of iterations * conv: error value used to evaluate convergence relative to tol * z: support scores of the GMM components ## Examples ```r X <- read.csv(system.file("test_data", "parasaurolophusA.txt", package="LOMAR", mustWork = TRUE), sep = "\t") Y <- read.csv(system.file("test_data", "parasaurolophusB.txt", package="LOMAR", mustWork = TRUE), sep = "\t") Z <- read.csv(system.file("test_data", "parasaurolophusC.txt", package="LOMAR", mustWork = TRUE), sep = "\t") PS <- list(X, Y, Z) C <- list() for(i in 1:3) { cv <- diag(0.1, ncol(PS[[i]])) + jitter(0.01, amount = 0.01) cv <- replicate(nrow(PS[[i]]), cv) C[[i]] <- cv } transformation <- jrmpc(PS, C = C, K = 100, maxIter = 20, tol = 0.01, model.selection = TRUE) ## Not run: # Visualize registration outcome library(rgl) colours <- c("blue", "green", "magenta") Yt <- transformation[['Y']] plot3d(Yt[[1]], col = colours[1]) for(i in 2:length(Yt)) { points3d(Yt[[i]], col = colours[i]) } # Visualize GMM centres highlighting those with high variance GMM <- as.data.frame(cbind(transformation[['M']], transformation[['S']])) colnames(GMM) <- c("x", "y", "z", "S") colours <- rep("blue", nrow(GMM)) # Find high variance components threshold <- quantile(transformation[['S']], 0.75) high.var.idx <- which(transformation[['S']]>threshold) colours[high.var.idx] <- "red" plot3d(GMM[, c("x", "y", "z")], col = colours, type = 's', size = 2, box = FALSE, xlab = '', ylab = '', zlab = '', xlim = c(-0.15,0.15), ylim = c(-0.15, 0.15), zlim = c(-0.15, 0.15)) ## End(Not run) ```

jrmpc function