jrmpc {LOMAR}

jrmpc

Description

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

Usage

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)

Value

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

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)