fit circle

Author: Jean-Romain

DESCRIPTION

@@ -2,7 +2,7 @@ Package: lidR
 Type: Package
 Title: Airborne LiDAR Data Manipulation and Visualization for Forestry
     Applications
-Version: 4.1.3
+Version: 4.2.0
 Authors@R: c(
     person("Jean-Romain", "Roussel", email = "[email protected]", role = c("aut", "cre", "cph")),
     person("David", "Auty", email = "", role = c("aut", "ctb"), comment = "Reviews the documentation"),
@@ -110,6 +110,7 @@ Collate:
     'engine_write.R'
     'fasterize.R'
     'filters.R'
+    'fit_shapes.R'
     'fullwaveform.R'
     'generate_las.R'
     'io_readLAS.R'

NAMESPACE

@@ -225,6 +225,7 @@ export(filter_poi)
 export(filter_single)
 export(filter_surfacepoints)
 export(find_trees)
+export(fit_circle)
 export(forest.colors)
 export(gap_fraction_profile)
 export(get_lidr_threads)

NEWS.md

@@ -9,6 +9,7 @@ v4.2.0 bring new tools for terrestrial data (TLS, MLS)
 - New: new C++ spatial indexing class `SparsePartition3D` for TLS data which is memory optimized
 - New: new functions `readALS` and `readTLS` that replace overly complex and unused `readALSLAS`, `readTLSLAS`, `readUAVLAS` and co.
 - New: new functions `readALScatalog` and `readTLScatalog` that replace overly complex and unused `readALSLAScatalog`, `readTLSLAScatalog`, `readUAVLAScatalog` and co.
+- New: new function `fit_circle` using RANSAC approach.
 - Fix: #771 read VPC files with absolute path
 - Enhance: `crs()` `is.empty()` and `area()` are now inherits from `terra` and no longer clash with `terra`.
 - Enhance: #776 `readLAScatalog` can skip corrupted files

R/fit_shapes.R

@@ -0,0 +1,135 @@
+fit_circle_on_3_points <- function(points_subset)
+{
+  stopifnot(nrow(points_subset) == 3L, ncol(points_subset) > 2L)
+
+  # Extract the coordinates
+  x1 <- points_subset[1, 1]
+  y1 <- points_subset[1, 2]
+  x2 <- points_subset[2, 1]
+  y2 <- points_subset[2, 2]
+  x3 <- points_subset[3, 1]
+  y3 <- points_subset[3, 2]
+
+  # Calculate the coefficients for the linear system
+  A <- 2 * (x2 - x1)
+  B <- 2 * (y2 - y1)
+  C <- x2^2 + y2^2 - x1^2 - y1^2
+  D <- 2 * (x3 - x1)
+  E <- 2 * (y3 - y1)
+  G <- x3^2 + y3^2 - x1^2 - y1^2
+
+  # Solve for a and b using Cramer's rule
+  denominator <- A * E - B * D
+  if (denominator == 0)
+  {
+    return(c(0, 0, 0))
+  }
+  a <- (C * E - B * G) / denominator
+  b <- (A * G - C * D) / denominator
+
+  # Calculate the radius
+  r <- sqrt((x1 - a)^2 + (y1 - b)^2)
+
+  # Return the center and radius
+  return(c(a, b, r))
+}
+
+#' Fits 2D Circles on a Point Cloud
+#'
+#' Fits a 2D horizontally-aligned circle to a set of 3D points. The method uses RANSAC-based fitting
+#' for robust estimation. The function returns a list with the circle parameters and additional data
+#' to help determine whether the points form a circular shape. While it is always possible to fit a
+#' circle to any dataset, the additional information assists in evaluating if the data genuinely
+#' represent a circular pattern. The root mean square error (RMSE) may not always be a reliable metric
+#' for assessing the quality of the fit due to non-circular elements (such as branches) that can arbitrarily
+#' increase the RMSE of an otherwise well-fitted circle, as shown in the example below. Therefore, the
+#' function also returns the angular range of the data, which indicates the spread of the inlier points:
+#' 360 degrees suggests a full circle, 180 degrees indicates a half-circle, or a smaller range may
+#' suggest a partial arc.
+#'
+#' @param points A LAS object representing a clustered slice, or an nx3 matrix of point coordinates.
+#' @param num_iteration The number of iterations for the RANSAC fitting algorithm.
+#' @param inlier_threshold A threshold value; points are considered inliers if their residuals are
+#' below this value.
+#'
+#' @return A list containing the circle parameters and additional information for determining whether
+#' the data fit a circular shape:
+#' - `center_x`, `center_y`, `radius`: parameters of the fitted circle.
+#' - `z`: average elevation of the circle.
+#' - `rmse`: root mean square error between the circle and all points.
+#' - `angle_range`: angular sector covered by inlier points.
+#' - `inliers`: IDs of the inlier points.
+#' @md
+#' @export
+#' @examples
+#' LASfile <- system.file("extdata", "dbh.laz", package="lidR")
+#' las <- readTLS(LASfile, select = "xyz")
+#' xyz = sf::st_coordinates(las)
+#' circle = fit_circle(xyz)
+#' plot(xyz, asp = 1, pch = 19, cex = 0.1)
+#' symbols(circle$center_x, circle$center_y, circles = circle$radius,
+#'   add = TRUE, fg = "red", inches = FALSE)
+#'
+#' trunk = las[circle$inliers]
+#'
+#' # Fitting a half-circle
+#' half = xyz[xyz[,1] > 101.45,]
+#' circle = fit_circle(half)
+#' plot(half, asp = 1, pch = 19, cex = 0.1)
+#' symbols(circle$center_x, circle$center_y, circles = circle$radius,
+#'   add = TRUE, fg = "red", inches = FALSE)
+#' circle$angle_range
+fit_circle <- function(points, num_iterations = 500, inlier_threshold = 0.01)
+{
+  best_circle <- NULL
+  max_inliers <- 0
+
+  if (is(points, "LAS")) points = st_coordinates(points)
+
+  stopifnot(is.matrix(points), ncol(points) == 3L, nrow(points) > 3L)
+
+  z = points[, 3]
+
+  for (i in 1:num_iterations)
+  {
+    # Randomly sample points
+    sample_indices <- sample(1:nrow(points), 3L)
+    points_subset <- points[sample_indices, ]
+
+    params <- fit_circle_on_3_points(points_subset)
+
+    # Compute residuals for all points
+    distances <- sqrt((points[, 1] - params[1])^2 + (points[, 2] - params[2])^2)
+    residuals <- abs(distances - params[3])
+
+    # Count inliers (points whose residuals are below the threshold)
+    inliers <- sum(residuals < inlier_threshold)
+
+    # Update best model if more inliers are found
+    if (inliers > max_inliers)
+    {
+      max_inliers <- inliers
+      best_circle <- params
+    }
+  }
+
+  center_x <- best_circle[1]
+  center_y <- best_circle[2]
+  radius <- best_circle[3]
+
+  # Goodness of fit
+  distances <- sqrt((points[, 1] - center_x)^2 + (points[, 2] - center_y)^2)
+  residuals <- abs(distances - radius)
+  inliers <- residuals < inlier_threshold
+  rmse <- sqrt(mean((residuals)^2))
+
+  # Angular range
+  angle_res = 3
+  angles <- atan2(points[inliers, 2] - center_y, points[inliers, 1] - center_x)
+  angles <- ifelse(angles < 0, angles + 2 * pi, angles)
+  angles <- sort(angles*180/pi)
+  rangles <- unique(round(angles/angle_res)*angle_res)
+  angle_range_degrees = sum(diff(rangles) <= angle_res)*angle_res
+
+  return(list(center_x = center_x, center_y = center_y, radius = radius, z = mean(z), rmse = rmse, angle_range = angle_range_degrees, inliers = which(inliers)))
+}