Package 'sosta'

Title: A package for the analysis of anatomical tissue structures in spatial omics data
Description: sosta (Spatial Omics STructure Analysis) is a package for analyzing spatial omics data to explore tissue organization at the anatomical structure level. It reconstructs morphologically relevant structures based on molecular features or cell types. It further calculates a range of structural and shape metrics to quantitatively describe tissue architecture. The package is designed to integrate with other packages for the analysis of spatial (omics) data.
Authors: Samuel Gunz [aut, cre] , Mark D. Robinson [aut, fnd]
Maintainer: Samuel Gunz <samuel.gunz@uzh.ch>
License: GPL (>= 3) + file LICENSE
Version: 0.99.5
Built: 2025-03-22 09:24:28 UTC
Source: https://github.com/bioc/sosta

Help Index

Function to estimate the intensity image of a point pattern

Description

Function to estimate the intensity image of a point pattern

Usage

.intensityImage(ppp, markSelect = NULL, bndw = NULL, dim)

Arguments

ppp

point pattern object of class ppp
markSelect

character; name of mark that is to be selected for the reconstruction
bndw

bandwidth of kernel density estimator
dim

numeric; x dimension of the final reconstruction.

Value

list; list with the intensity image and the bandwidth and dimension parameters

Function to estimate the intensity threshold for the reconstruction of spatial structures

Description

Function to estimate the intensity threshold for the reconstruction of spatial structures

Usage

.intensityThreshold(densityImage, steps = 250)

Arguments

densityImage

real-valued pixel image; output from the function .intensityImage
steps

numeric; value used to filter the density estimates, where only densities greater than the maximum value divided by threshold are considered. Default is 250.

Value

numeric; estimated threshold

Function to assign spatial points to structures

Description

This function assigns each spatial point in a SpatialExperiment object (spe) to the first intersecting structure from a given set of spatial structures.

Usage

assingCellsToStructures(
  spe,
  allStructs,
  imageCol,
  uniqueId = "structID",
  nCores = 1
)

Arguments

spe

SpatialExperiment; An object of class SpatialExperiment containing spatial point data.
allStructs

sf; A simple feature collection (sf object) representing spatial structures. Must contain a column which contains a unique identifier for each structure. Default = structID.
imageCol

character; The column name in spe and allStructs that identifies the corresponding image.
uniqueId

character; The column name in the simple feature collection for which to compute the assignment.
nCores

integer; The number of cores to use for parallel processing (default is 1).

Value

A vector with structure assignments for each spatial point in spe. Points that do not overlap with any structure are assigned NA.

Examples

library("SpatialExperiment")
data("sostaSPE")
allStructs <- reconstructShapeDensitySPE(sostaSPE,
    marks = "cellType", imageCol = "imageName",
    markSelect = "A", bndw = 3.5, thres = 0.045
)
colData(sostaSPE)$structAssign <- assingCellsToStructures(
    sostaSPE,
    allStructs, "imageName"
)
if (require("ggplot2")) {
    cbind(
        colData(sostaSPE[, sostaSPE[["imageName"]] == "image1"]),
        spatialCoords(sostaSPE[, sostaSPE[["imageName"]] == "image1"])
    ) |>
        as.data.frame() |>
        ggplot(aes(x = x, y = y, color = structAssign)) +
        geom_point(size = 0.25) +
        coord_equal()
}

Converts a binary matrix to an sf polygon

Description

Converts a binary matrix to an sf polygon

Usage

binaryImageToSF(binaryMatrix, xmin, xmax, ymin, ymax)

Arguments

binaryMatrix

matrix; binary matrix
xmin

integer; minimum x coordinate of the coordinate system
xmax

integer; maximum x coordinate of the coordinate system
ymin

integer; minimum y coordinate of the coordinate system
ymax

integer; maximum y coordinate of the coordinate system

Value

sf object

Examples

matrixR <- matrix(c(
    0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0
), nrow = 9, byrow = TRUE)
polyR <- binaryImageToSF(matrixR, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
plot(polyR)

Calculate the proportion of each cell type within spatial structures

Description

Calculate the proportion of each cell type within spatial structures

Usage

cellTypeProportions(spe, structColumn, cellTypeColumn, nCores = 1)

Arguments

spe

SpatialExperiment object
structColumn

character; name of the colData column specifying the structure assignments
cellTypeColumn

character; name of the colData column specifying cell types
nCores

integer; The number of cores to use for parallel processing (default is 1).

Value

A data frame where rows correspond to unique structures and columns correspond to cell types, containing the proportion of each cell type within each structure.

Examples

library("SpatialExperiment")
data("sostaSPE")
allStructs <- reconstructShapeDensitySPE(sostaSPE,
    marks = "cellType", imageCol = "imageName",
    markSelect = "A", bndw = 3.5, thres = 0.045
)
colData(sostaSPE)$structAssign <- assingCellsToStructures(
    sostaSPE,
    allStructs, "imageName"
)
cellTypeProportions(sostaSPE, "structAssign", "cellType")

Create a Point Pattern on a Simulated Tissue Image

Description

This function generates a spatial point pattern with different types of points (A, B, C) distributed over the simulated tissue structure.

Usage

createPointPatternTissue(tissueImage, intA, intB, intCInA, intCInB)

Arguments

tissueImage

Matrix; A binary matrix representing the simulated tissue.
intA

Numeric; Intensity of type "A" points (points per unit area) on tissue regions.
intB

Numeric; Intensity of type "B" points (points per unit area) on non-tissue regions.
intCInA

Numeric; Intensity of type "C" points placed in extended regions around tissue.
intCInB

Numeric; Intensity of type "C" points placed within tissue.

Value

A ppp object representing the spatial point pattern.

Examples

tissueImage <- simulateTissueBlobs(128, 100, 7)
createPointPatternTissue(tissueImage, 0.1, 0.1, 0.005, 0.005)

Estimate reconstruction parameters from a set of images

Description

Estimate reconstruction parameters from a set of images

Usage

estimateReconstructionParametersSPE(
  spe,
  marks,
  imageCol,
  markSelect = NULL,
  nImages = NULL,
  fun = "bw.diggle",
  dim = 500,
  nCores = 1,
  plotHist = TRUE
)

Arguments

spe

SpatialExperiment; a object of class SpatialExperiment
marks

character; name of column in colData that will correspond to the ppp marks
imageCol

character; name of a column in colData that corresponds to the image
markSelect

character; name of mark that is to be selected for the reconstruction
nImages

integer; number of images for the estimation. Will be randomly sampled
fun

character; function to estimate the kernel density. Default bw.diggle.
dim

numeric; x dimension of the final reconstruction. A lower resolution speed up computation but lead to less exact reconstruction. Default = 500
nCores

numeric; number of cores for parallel processing using mclapply. Default = 1
plotHist

logical; if histogram of estimated densities and thresholds should be plotted. Default = TRUE

Value

tibble; tibble with estimated intensities and thresholds

Examples

data("sostaSPE")
estimateReconstructionParametersSPE(sostaSPE,
    marks = "cellType", imageCol = "imageName",
    markSelect = "A", plotHist = TRUE
)

Estimate the intensity threshold for the reconstruction of spatial structures

Description

Estimate the intensity threshold for the reconstruction of spatial structures

Usage

findIntensityThreshold(ppp, markSelect = NULL, bndw = NULL, dim, steps = 250)

Arguments

ppp

point pattern object of class ppp
markSelect

character; name of mark that is to be selected for the reconstruction
bndw

numeric; bandwith of the sigma parameter in the density estimation, if no value is given the bandwith is estimated using cross validation with the bw.diggle function.
dim

numeric; x dimension of the final reconstruction.
steps

numeric; value used to filter the density estimates, where only densities greater than the maximum value divided by threshold are considered. Default is 250.

Value

numeric; estimated intensity threshold

Examples

data(sostaSPE)
ppp <- SPE2ppp(sostaSPE, marks = "cellType", imageCol = "imageName", imageId = "image1")
findIntensityThreshold(ppp, markSelect = "A", dim = 250)

Function to get the dimension based on dim of y axis

Description

Function to get the dimension based on dim of y axis

Usage

getDimXY(ppp, ydim)

Arguments

ppp

point pattern object of class ppp
ydim

dimension of y axis

Value

vector; vector with x and y dimension

Examples

data(sostaSPE)
pp <- SPE2ppp(sostaSPE,
    marks = "cellType", imageCol = "imageName",
    imageId = "image1"
)
getDimXY(pp, 500)

Calculate mean shape metrics of a set of polygons

Description

Calculate mean shape metrics of a set of polygons

Usage

meanShapeMetrics(totalShapeMetricMatrix)

Arguments

totalShapeMetricMatrix

matrix of shape metrics

Value

matrix; matrix of mean shape metrics

Examples

data(sostaSPE)
struct <- reconstructShapeDensityImage(sostaSPE,
    marks = "cellType", imageCol = "imageName",
    imageId = "image1", markSelect = "A", dim = 500
)
shapeMetrics <- totalShapeMetrics(struct)
meanShapeMetrics(shapeMetrics)

Compute minimum boundary distances for each cell within its corresponding image structures

Description

Compute minimum boundary distances for each cell within its corresponding image structures

Usage

minBoundaryDistances(spe, imageColumn, structColumn, allStructs, nCores = 1)

Arguments

spe

SpatialExperiment object
imageColumn

character; name of the colData column specifying the image name
structColumn

character; name of the colData column specifying structure assignments
allStructs

sf object; contains spatial structures with corresponding image names
nCores

integer; The number of cores to use for parallel processing (default is 1).

Value

A numeric vector containing the minimum distances between cells and structure boundaries, values within structures have negative values.

Examples

library("SpatialExperiment")
data("sostaSPE")
allStructs <- reconstructShapeDensitySPE(sostaSPE,
    marks = "cellType", imageCol = "imageName",
    markSelect = "A", bndw = 3.5, thres = 0.045
)
colData(sostaSPE)$structAssign <- assingCellsToStructures(
    sostaSPE,
    allStructs, "imageName"
)
colData(sostaSPE)$minDist <- minBoundaryDistances(
    sostaSPE,
    "imageName", "structAssign", allStructs
)
if (require("ggplot2")) {
    cbind(colData(sostaSPE), spatialCoords(sostaSPE)) |>
        as.data.frame() |>
        ggplot(aes(x = x, y = y, color = minDist)) +
        geom_point(size = 0.25) +
        scale_colour_gradient2() +
        geom_sf(data = allStructs, fill = NA, inherit.aes = FALSE) +
        facet_wrap(~imageName)
}

Function to normalize coordinates between zero and one while keep scaling

Description

Function to normalize coordinates between zero and one while keep scaling

Usage

normalizeCoordinates(coords)

Arguments

coords

matrix; matrix with coordinates

Value

matrix; coordinates scaled between 0 and 1

Examples

matrixR <- matrix(c(
    0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0
), nrow = 9, byrow = TRUE)
coords <- xyCoordinates(matrixR)
normalizeCoordinates(coords)

Reconstruct polygon from point pattern density

Description

This function estimates the density of a spatial point pattern (ppp), thresholds the density to create a binary image, and then converts it to a valid sf object (polygons).

Usage

reconstructShapeDensity(ppp, markSelect = NULL, bndw = NULL, thres = NULL, dim)

Arguments

ppp

point pattern object of class ppp
markSelect

character; name of mark that is to be selected for the reconstruction
bndw

bandwidth of kernel density estimator
thres

intensity threshold for the reconstruction
dim

numeric; x dimension of the final reconstruction.

Value

sf object of class POLYGON

Examples

data("sostaSPE")
ppp <- SPE2ppp(sostaSPE, marks = "cellType", imageCol = "imageName", imageId = "image1")
thres <- findIntensityThreshold(ppp, markSelect = "A", dim = 500)
struct <- reconstructShapeDensity(ppp, markSelect = "A", thres = thres, dim = 500)
plot(struct)

Reconstruct structure from spe object with given image id

Description

Reconstruct structure from spe object with given image id

Usage

reconstructShapeDensityImage(
  spe,
  marks,
  imageCol,
  imageId,
  markSelect,
  dim = 500,
  bndw = NULL,
  thres = NULL
)

Arguments

spe

SpatialExperiment; a object of class SpatialExperiment
marks

character; name of column in colData that will correspond to the ppp marks
imageCol

character; name of a column in colData that corresponds to the image
imageId

character; image id, must be present in imageCol
markSelect

character; name of mark that is to be selected for the reconstruction
dim

numeric; x dimension of the final reconstruction. A lower resolution speed up computation but lead to less exact reconstruction. Default = 500
bndw

numeric; smoothing bandwidth in the density estimation, corresponds to the sigma parameter in the density.ppp function, if no value is given the bandwidth is estimated using cross validation with the bw.diggle function.
thres

numeric; intensity threshold for the reconstruction; if NULL the threshold is set as the mean between the mode of the pixel intensity distributions

Value

sf object of class POLYGON

Examples

data("sostaSPE")
struct <- reconstructShapeDensityImage(sostaSPE,
    marks = "cellType", imageCol = "imageName", imageId = "image1",
    markSelect = "A", dim = 500
)
plot(struct)

Reconstruct structure from spatial experiment object per image id

Description

Reconstruct structure from spatial experiment object per image id

Usage

reconstructShapeDensitySPE(
  spe,
  marks,
  imageCol,
  markSelect,
  dim = 500,
  bndw = NULL,
  thres = NULL,
  nCores = 1
)

Arguments

spe

SpatialExperiment; a object of class SpatialExperiment
marks

character; name of column in colData that will correspond to the ppp marks
imageCol

character; name of a column in colData that corresponds to the image
markSelect

character; name of mark that is to be selected for the reconstruction
dim

numeric; x dimension of the final reconstruction. A lower resolution speed up computation but lead to less exact reconstruction. Default = 500
bndw

numeric; bandwidth of the sigma parameter in the density estimation, if no value is given the bandwidth is estimated using cross validation with the bw.diggle function for each image individually.
thres

numeric; intensity threshold for the reconstruction; if NULL the threshold is set as the mean between the mode of the pixel intensity distributions estimated for each image individual
nCores

numeric; number of cores for parallel processing using mclapply. Default = 1

Value

simple feature collection

Examples

data("sostaSPE")
allStructs <- reconstructShapeDensitySPE(sostaSPE,
    marks = "cellType", imageCol = "imageName",
    markSelect = "A", bndw = 3.5, thres = 0.005
)
allStructs

Intensity plot

Description

This function plots the intensity of a point pattern image and displays a histogram of the intensity values. Note that intensities less than largest intensity value divided by 250 are not displayed in the histogram.

Usage

shapeIntensityImage(
  spe,
  marks,
  imageCol,
  imageId,
  markSelect,
  bndw = NULL,
  dim = 500
)

Arguments

spe

SpatialExperiment; a object of class SpatialExperiment
marks

character; name of column in colData that will correspond to the ppp marks
imageCol

character; name of a column in colData that corresponds to the image
imageId

character; image id, must be present in imageCol
markSelect

character; name of mark that is to be selected for the reconstruction
bndw

numeric; smoothing bandwidth in the density estimation, corresponds to the sigma parameter in the density.ppp function, if no value is given the bandwidth is estimated using cross validation with the bw.diggle function.
dim

numeric; x dimension of the final reconstruction. A lower resolution speeds up computation but lead to less exact reconstruction. Default = 500

Value

ggplot object with intensity image and histogram

Examples

data("sostaSPE")
shapeIntensityImage(sostaSPE,
    marks = "cellType", imageCol = "imageName",
    imageId = "image1", markSelect = "A"
)

Calculate a set of shape metrics of a polygon

Description

Calculate a set of shape metrics of a polygon

Usage

shapeMetrics(sfPoly)

Arguments

sfPoly

POLYGON of class sfc

Value

list; list of shape metrics

Examples

matrix_R <- matrix(c(
    0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0
), nrow = 9, byrow = TRUE)
polyR <- binaryImageToSF(matrix_R, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
shapeMetrics(polyR)

Simulate Tissue Blobs

Description

This function generates a simulated tissue-like structure using a Gaussian blur technique.

Usage

simulateTissueBlobs(size, seedNumber, clumpSize)

Arguments

size

Integer; The size (width and height) of the simulated tissue image.
seedNumber

Integer; The number of random seed points used to generate tissue blobs.
clumpSize

Numeric; The standard deviation (sigma) of the Gaussian blur applied to generate tissue clumps.

Value

A binary matrix representing the simulated tissue structure.

Examples

tissueImage <- simulateTissueBlobs(128, 100, 7)
image(tissueImage)

Example SpatialExperiment Object with Simulated Tissue Images and Point Patterns

Description

This dataset contains a simulated SpatialExperiment object (sostaSPE) representing three tissue images, each with a corresponding spatial point pattern. The point patterns contain different cell types (A, B, and C), distributed according to simulated tissue structures.

Usage

sostaSPE

Format

A SpatialExperiment object with the following structure:

x

Numeric; x-coordinate of each point (cell location).

y

Numeric; y-coordinate of each point (cell location).

cell_type

Factor; Cell type assigned to each point (A, B, or C).

image_name

Factor; Identifier for the tissue image (image1, image2, or image3).

Details

The dataset was generated as follows:

  • Three tissue images were simulated using simulateTissueBlobs().

  • Spatial point patterns were created for each tissue using createPointPatternTissue().

  • The point pattern data was converted into a SpatialExperiment object with spatial coordinates.

Function to convert spatialCoords to an sf object

Description

Function to convert spatialCoords to an sf object

Usage

spatialCoords2SF(spe)

Arguments

spe

SpatialExperiment; a object of class SpatialExperiment

Value

sf; Simple feature collection of geometry type POINT

Examples

data(sostaSPE)
speSel <- sostaSPE[, sostaSPE[["imageName"]] == "image1"]
spatialCoords2SF(speSel)

Function to convert spatial coordinates of a SpatialExperiment object to a ppp object

Description

Function to convert spatial coordinates of a SpatialExperiment object to a ppp object

Usage

SPE2ppp(spe, marks, imageCol = NULL, imageId = NULL)

Arguments

spe

SpatialExperiment; a object of class SpatialExperiment
marks

character; name of column in colData that will correspond to the ppp marks
imageCol

character; name of a column in colData that corresponds to the image
imageId

character; image id, must be present in imageCol

Value

ppp; object of type ppp

Examples

data(sostaSPE)
SPE2ppp(sostaSPE,
    marks = "cellType", imageCol = "imageName",
    imageId = "image1"
)

Calculate curvature of sf object

Description

Calculate curvature of sf object

Usage

stCalculateCurvature(sfPoly, smoothness = 5)

Arguments

sfPoly

POLYGON of class sf
smoothness

list; curvature measures

Value

list; list of curvatures values

References

https://stackoverflow.com/questions/62250151/calculate-curvature-of-a-closed-object-in-r

Examples

matrixR <- matrix(c(
    0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0
), nrow = 9, byrow = TRUE)
polyR <- binaryImageToSF(matrixR, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
stCalculateCurvature(polyR)

Calculate curl of a polygon

Description

Calculate curl of a polygon

Usage

stCalculateShapeCurl(sfPoly)

Arguments

sfPoly

POLYGON of class sf

Value

numeric; the curl of the polygon

Examples

matrixR <- matrix(c(
    1, 1, 1, 1, 1, 0,
    1, 1, 0, 0, 1, 1,
    1, 1, 0, 0, 1, 1,
    1, 1, 1, 1, 1, 0,
    1, 1, 0, 1, 1, 0,
    1, 1, 0, 0, 1, 1,
    1, 1, 0, 0, 1, 1
), nrow = 7, byrow = TRUE)
polyR <- binaryImageToSF(matrixR, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
stCalculateShapeCurl(polyR)

Calculate the length of feature axes of an sf polygon

Description

Calculate the length of feature axes of an sf polygon

Usage

stFeatureAxes(sfPoly)

Arguments

sfPoly

POLYGON of class sf

Value

list; list containing the major and minor axis lengths

Examples

matrixR <- matrix(c(
    0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0
), nrow = 9, byrow = TRUE)
polyR <- binaryImageToSF(matrixR, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
stFeatureAxes(polyR)

Calculate a set of shape metrics of a set of polygons

Description

Calculate a set of shape metrics of a set of polygons

Usage

totalShapeMetrics(sfInput)

Arguments

sfInput

MULTIPOLYGON of class sf

Details

Calculate a set of shape metrics of a set of polygons. The function calculates all metrics that are implemented in the function shapeMetrics()

Value

matrix; matrix of shape metrics

Examples

data(sostaSPE)
struct <- reconstructShapeDensityImage(sostaSPE,
    marks = "cellType", imageCol = "imageName",
    imageId = "image1", markSelect = "A", dim = 500
)
totalShapeMetrics(struct)

Function to extract x y coordinates from binary image

Description

Function to extract x y coordinates from binary image

Usage

xyCoordinates(inputMatrix)

Arguments

inputMatrix

a binary matrix

Value

matrix; matrix with x,y coordinates of the cell of the input matrix

Examples

matrixR <- matrix(c(
    0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 1, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 1, 1, 0, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 1, 1, 0, 0, 1, 1, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0
), nrow = 9, byrow = TRUE)
xyCoordinates(matrixR)