# Estimation of the likelihood of a bone section Estimation of the compactness of a bone section using radial model. If the fitted.parameters and fixed.parameters are NULL and the analysis includes a BP_FitMLCompactness() result, the values of this result is used as a reference for fitted.parameters and fixed.parameters. If no BP_FitMLCompactness() result is available, it will use: fitted.parameters=c(P=0.5, S=0.05, Min=-2, Max=5); fixed.parameters=c(K1=1, K2=1). The reference for radial estimation of compactness is the trigonometric circle for rotation.angle=0 in BP_EstimateCompactness(): * The top of the section is located at -pi/2. * The left of the section is located at -pi and +pi. * The bottom of the section is located at pi/2. * The right of the section is 0. If rotation.angle is different from 0, the value of rotation.angle is added to the angle modulo 2.pi. The two-steps analysis performs first a quasi-Newton method, then a Bayesian MCMC and finally again a quasi-Newton method. It generally ensures that global minimum is found. On the other hand, it doubles the time to complete for each angle. To control the parallel computing, use: options(mc.cores = [put here the number of cores you want use]) options(forking = FALSE) or options(forking = TRUE) The maximum number of cores is obtained by: parallel::detectCores() ```r BP_FitMLRadialCompactness( bone, fitted.parameters = NULL, priors = NULL, fixed.parameters = NULL, analysis = 1, silent = FALSE, twosteps = TRUE, progressbar = FALSE ) ``` ## Arguments - `bone`: The bone image to be used - `fitted.parameters`: Parameters of the model to be fitted - `priors`: If twosteps is TRUE, tell what prior should be used. - `fixed.parameters`: Fixed parameters of the model - `analysis`: Name or rank of analysis - `silent`: Should the function displays some information? - `twosteps`: Should a 2-steps analysis be performed? - `progressbar`: Should a progress bar be shown? ## Returns The -Ln L ## Details BP_FitMLRadialCompactness estimates likelihood of model of a bone section ## Examples ```r ## Not run: # Not run library(BoneProfileR) path_Hedgehog <- system.file("extdata", "Erinaceus_europaeus_fem_2-1_small.png", package = "BoneProfileR") bone <- BP_OpenImage(file=path_Hedgehog) # or bone <- BP_OpenImage(ijtiff=TRUE) bone <- BP_DetectBackground(bone=bone, analysis="logistic") bone <- BP_DetectForeground(bone=bone, analysis="logistic") bone <- BP_DetectCenters(bone=bone, analysis="logistic") bone <- BP_EstimateCompactness(bone, analysis="logistic") bone <- BP_EstimateCompactness(bone, analysis="logistic", cut.angle=30) bone <- BP_FitMLCompactness(bone, analysis="logistic") plot(bone) plot(bone, type="observations") plot(bone, type="observations+model", analysis=1) fittedpar <- BP_GetFittedParameters(bone, analysis="logistic", ML=TRUE, return.all = FALSE)[, "mean"] bone <- BP_DuplicateAnalysis(bone, from="logistic", to="flexit") bone <- BP_FitMLCompactness(bone, fitted.parameters=c(fittedpar, K1=1.01, K2=1.01), fixed.parameters=NULL, analysis="flexit") bone <- BP_FitBayesianCompactness(bone, analysis="flexit") mcmc <- RM_get(bone, RMname = "flexit", value="mcmc") fittedpar <- as.parameters(mcmc) bone <- BP_FitMLCompactness(bone, fitted.parameters=fittedpar, fixed.parameters=NULL, analysis="flexit") compare_AIC(Logistic=BP_GetFittedParameters(bone, analysis="logistic", ML=TRUE, return.all = TRUE), Flexit=BP_GetFittedParameters(bone, analysis="flexit", ML=TRUE, return.all=TRUE)) out4p <- plot(bone, type="observations+model", analysis="logistic") out6p <- plot(bone, type="observations+model", analysis="flexit") # The twosteps fit is more acurate but is around 100 times slower bone <- BP_FitMLRadialCompactness(bone, analysis="logistic", twosteps=TRUE) bone <- BP_FitMLRadialCompactness(bone, analysis="logistic", twosteps=FALSE) plot(bone, type="observations", angle=0) plot(bone, type="model", analysis="logistic", angle=0) plot(bone, type="observations+model", angle=0) plot(bone, type="observations+model", angle=pi) plot(bone, type="radial", parameter.name=c("P"), analysis="logistic") plot(bone, type="radial", parameter.name=c("P", "S"), analysis="logistic") plot(bone, type="radial", parameter.name=c("P", "S", "Min", "Max"), analysis="logistic") plot(bone, type="radial", parameter.name=c("TRC"), analysis="logistic") # The observed compactness plot(bone, type="radial", parameter.name=c("observed.compactness"), analysis="logistic") # The observed compactness weighted by the pixel number plot(bone, type="radial", parameter.name="linearized.observed.compactness", analysis="logistic") # The integration of the compactness model plot(bone, type="radial", parameter.name="modeled.compactness", analysis="logistic") # The integration of the compactness model weighted by the pixel number plot(bone, type="radial", parameter.name="linearized.modeled.compactness", analysis="logistic") # Test using the change of orientation using default.angle from BP_EstimateCompactness(): bone <- BP_DuplicateAnalysis(bone, from="logistic", to="logistic_rotation_pi") # With a pi rotation, the top moves to the bottom and the left moves to the right bone <- BP_EstimateCompactness(bone, rotation.angle=pi, analysis="logistic_rotation_pi") bone <- BP_FitMLRadialCompactness(bone, analysis="logistic_rotation_pi") plot(bone, type="radial", parameter.name=c("P", "S"), analysis="logistic") plot(bone, type="radial", parameter.name=c("P", "S"), analysis="logistic_rotation_pi") BP_Report(bone=bone, analysis=1, docx=NULL, pdf=NULL, xlsx=file.path(getwd(), "report.xlsx"), author="Marc Girondot", title=attributes(bone)$name) ## End(Not run) ``` ## See Also Other BoneProfileR: `BP_AutoFit()`, `BP_ChooseBackground()`, `BP_ChooseCenter()`, `BP_ChooseForeground()`, `BP_DetectBackground()`, `BP_DetectCenters()`, `BP_DetectForeground()`, `BP_DuplicateAnalysis()`, `BP_EstimateCompactness()`, `BP_FitBayesianCompactness()`, `BP_FitBayesianPeriodicCompactness()`, `BP_FitMLCompactness()`, `BP_FitMLPeriodicCompactness()`, `BP_GetFittedParameters()`, `BP_ListAnalyses()`, `BP_LnLCompactness()`, `BP_OpenImage()`, `BP_Report()`, `Erinaceus_europaeus`, `plot.BoneProfileR()`, `summary.BoneProfileR()` ## Author(s) Marc Girondot marc.girondot@gmail.com

BP_FitMLRadialCompactness function