diff --git a/R/CTutils.R b/R/CTutils.R
index 15736006..368d17ce 100644
--- a/R/CTutils.R
+++ b/R/CTutils.R
@@ -3,6 +3,9 @@
 #' @aliases axes CTlist CTname CTtype CTdata addCT rmvCT
 #' 
 #' @param x \code{SpatialData}, an element, or \code{SpatialDataAttrs}.
+#' @param y NULL (default) returns a list where each element is 
+#'   an axis: a list with name/type/unit (e.g., x/space/micrometer);
+#'   \code{y="name/type/unit"} extracts specific data over all axiis.
 #' @param i for \code{CTpath}, source node label; else, string or 
 #'   scalar integer giving the name or index of a coordinate space.
 #' @param name character(1); name of coordinate space
@@ -51,11 +54,13 @@ NULL
 
 #' @rdname CTutils
 #' @export
-setMethod("axes", "SpatialDataAttrs", \(x, ...) {
+setMethod("axes", "SpatialDataAttrs", \(x, y=NULL, ...) {
     ms <- multiscales(x)
     if (!is.null(ms)) x <- ms[[1]]
     if (is.null(x <- x$axes)) stop("couldn't find 'axes'") 
-    return(x)
+    if (is.null(y)) return(x)
+    y <- match.arg(y, c("name", "type", "unit"))
+    vapply(x, `[[`, character(1), y)
 })
 
 # CTlist/data/type/name() ----
@@ -105,7 +110,7 @@ setMethod("CTname", "SpatialDataAttrs", \(x, ...) {
 
 #' @rdname CTutils
 #' @export
-setMethod("axes", "SpatialDataElement", \(x, ...) axes(meta(x), ...))
+setMethod("axes", "SpatialDataElement", \(x, y=NULL, ...) axes(meta(x), y, ...))
 
 #' @rdname CTutils
 #' @export
diff --git a/R/centroids.R b/R/centroids.R
index cd7ac93f..b9fb3d28 100644
--- a/R/centroids.R
+++ b/R/centroids.R
@@ -36,18 +36,34 @@ setMethod("centroids", "SpatialDataLabel", \(x,
     as=c("data.frame", "matrix")) {
     as <- match.arg(as)
     y <- data(x)
+    if (length(dim(y)) > 2) {
+        # max-projection
+        ax <- match(c("y", "x"), axes(x, "name"))
+        y <- apply(y, ax, max)
+    }
     y <- as(y, "dgCMatrix")
     i <- summary(y)
     # flip dimensions so that columns=x, rows=y
-    # TODO: should these be offset by 0.5?
     i[, c(1, 2)] <- i[, c(2, 1)]-0.5
     xy <- tapply(i[, -3], i[[3]], colMeans)
     xy <- do.call(rbind, xy)
     xy <- cbind(xy, as.integer(rownames(xy)))
     dimnames(xy) <- list(NULL, c("x", "y", "i"))
+    # multi-scale adjustment
+    sf <- .get_multiscale_scale(x)
+    xy[,1] <- xy[,1]*tail(sf, 1)
+    xy[,2] <- xy[,2]*tail(sf, 2)[1]
+    # offset
+    wh <- metadata(x)$wh
+    if (!is.null(wh)) {
+        xy[,1] <- xy[,1]+wh[[1]][1]
+        xy[,2] <- xy[,2]+wh[[2]][1]
+    }
+    # output
     if (as == "matrix") return(xy)
     xy <- as.data.frame(xy)
-    xy$i <- factor(xy$i); xy
+    xy$i <- factor(xy$i)
+    return(xy)
 })
 
 #' @export
diff --git a/man/CTutils.Rd b/man/CTutils.Rd
index 3e28c3d2..e8a33d6d 100644
--- a/man/CTutils.Rd
+++ b/man/CTutils.Rd
@@ -26,7 +26,7 @@
 \alias{addCT,SpatialDataAttrs-method}
 \title{Coord. trans. utilities}
 \usage{
-\S4method{axes}{SpatialDataAttrs}(x, ...)
+\S4method{axes}{SpatialDataAttrs}(x, y = NULL, ...)
 
 \S4method{CTlist}{SpatialDataAttrs}(x, ...)
 
@@ -36,7 +36,7 @@
 
 \S4method{CTname}{SpatialDataAttrs}(x, ...)
 
-\S4method{axes}{SpatialDataElement}(x, ...)
+\S4method{axes}{SpatialDataElement}(x, y = NULL, ...)
 
 \S4method{CTlist}{SpatialDataElement}(x, ...)
 
@@ -59,6 +59,10 @@
 \arguments{
 \item{x}{\code{SpatialData}, an element, or \code{SpatialDataAttrs}.}
 
+\item{y}{NULL (default) returns a list where each element is 
+an axis: a list with name/type/unit (e.g., x/space/micrometer);
+\code{y="name/type/unit"} extracts specific data over all axiis.}
+
 \item{...}{option arguments passed to and from other methods.}
 
 \item{i}{for \code{CTpath}, source node label; else, string or