imregionalmax

Regional maxima

Description

BW = imregionalmax(I)

Returns the binary image BW that identifies the regional maxima in the 2-D grayscale image I. Regional maxima are connected components of pixels with a constant intensity value, surrounded by pixels with a lower value.

BW = imregionalmax(I, conn)

Computes the regional maxima using the specified connectivity conn.

Input Arguments

I — GMTgrid|image or Matrix

Grayscale 2-D image, specified as a numeric matrix.

Data Types: UInt8 and Floating point types. In this later case an UInt8 representation is used internally.

conn — Pixel connectivity

Pixel connectivity, specified as one of the values in this table. The default connectivity is 8 for 2-D images.

Two-Dimensional Connectivities

Connectivity can also be defined by specifying a 3-by-3 matrix of 0s and 1s. The 1-valued elements define neighborhood locations relative to the center element of conn. Note that conn must be symmetric about its center element.

Data Types: Int, or array of Bool

Output Arguments

BW — GMTimage with locations of regional minima

Locations of regional maxima, returned as a logical array of the same size as I. Pixels with the value true (or 1) indicate regional maxima; all other pixels are set to false (or 0).

Data Types: Bool

Notes

Regional Maxima vs. Local Maxima: A regional maximum is a connected component of pixels with constant intensity, all of whose neighbors have a strictly lower value. This is different from a local maximum, which is a single pixel whose value is greater than or equal to all its neighbors.

Flat Regions: If an image contains large flat regions at the maximum intensity level, the entire flat region will be marked as a regional maximum.

Connectivity Impact: Higher connectivity values (e.g., 8 vs 4 in 2-D) can merge what would be separate regional maxima under lower connectivity, reducing the total number of detected maxima.

Noise Sensitivity: imregionalmax can be sensitive to noise and may detect many spurious maxima. Consider preprocessing with imhmax (h-maxima transform) or post-processing with bwareaopen to remove small or shallow maxima.

Tips

• Use imhmax to suppress shallow regional maxima before detection

• Apply bwareaopen to remove small spurious regional maxima

• Combine with watershed for marker-based image segmentation

• For elevation data, regional maxima identify peaks and summits

• Use imextendedmax to apply the H-maxima transform and find regional maxima in one step

• The complement operation can be used to find regional minima: imregionalmax(-I) or use imregionalmin(I)

Examples

Find Regional Maxima in Simple Array

Create a simple sample array with several regional maxima:

A = 10 * ones(10, 10)
A[2:4, 2:4] .= 22
A[6:8, 6:8] .= 33
A[2, 7] = 44
A[3, 8] = 45
A[4, 9] = 44

Output:

10×10 Matrix{Float64}:
 10.0  10.0  10.0  10.0  10.0  10.0  10.0  10.0  10.0  10.0
 10.0  22.0  22.0  22.0  10.0  10.0  44.0  10.0  10.0  10.0
 10.0  22.0  22.0  22.0  10.0  10.0  10.0  45.0  10.0  10.0
 10.0  22.0  22.0  22.0  10.0  10.0  10.0  10.0  44.0  10.0
 10.0  10.0  10.0  10.0  10.0  10.0  10.0  10.0  10.0  10.0
 10.0  10.0  10.0  10.0  10.0  33.0  33.0  33.0  10.0  10.0
 10.0  10.0  10.0  10.0  10.0  33.0  33.0  33.0  10.0  10.0
 10.0  10.0  10.0  10.0  10.0  33.0  33.0  33.0  10.0  10.0
 10.0  10.0  10.0  10.0  10.0  10.0  10.0  10.0  10.0  10.0
 10.0  10.0  10.0  10.0  10.0  10.0  10.0  10.0  10.0  10.0

Calculate the regional maxima. The function returns a binary image, the same size as the input image, in which pixels with the value true (or 1) represent the regional maxima. imregionalmax sets all other pixels to false (or 0):

regmax = imregionalmax(A)

Output:

10×10 BitMatrix:
 0  0  0  0  0  0  0  0  0  0
 0  1  1  1  0  0  0  0  0  0
 0  1  1  1  0  0  0  1  0  0
 0  1  1  1  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  1  1  1  0  0
 0  0  0  0  0  1  1  1  0  0
 0  0  0  0  0  1  1  1  0  0
 0  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0

Note that the pixel at position (3, 8) with value 45 is identified as a regional maximum because it is higher than all its neighbors.

Find Regional Maxima in Grayscale Image

Load a grayscale image:

I = gmtread("coins.png")
imshow(I)

Find the regional maxima:

BW = imregionalmax(I)
imshow(BW)

Overlay the regional maxima on the original image:

# Create an overlay showing maxima in green
imshow(I)
overlay!(BW, color=:green)

Compare Different Connectivity Settings

Create a test image with a ridge structure:

# Create an image with a ridge
I = zeros(UInt8, 15, 15)
I[8, :] .= 100  # Horizontal ridge
I[:, 8] .= 100  # Vertical ridge
I[8, 8] = 150   # Peak at intersection

Compute regional maxima with different connectivity:

# 4-connectivity (edges only)
BW4 = imregionalmax(I, 4)

# 8-connectivity (edges and corners)
BW8 = imregionalmax(I, 8)

# Display results
subplot(1, 3, 1)
imshow(I)
title!("Original Image")

subplot(1, 3, 2)
imshow(BW4)
title!("4-Connectivity")

subplot(1, 3, 3)
imshow(BW8)
title!("8-Connectivity")

showfig()

Use Regional Maxima for Marker-Based Watershed Segmentation

Regional maxima are often used to identify seed points for marker-based watershed segmentation:

# Load image
I = gmtread("coins.png")

# Compute distance transform
D = bwdist(.!imbinarize(I))

# Find regional maxima in distance transform
maxima = imregionalmax(D)

# Remove small regional maxima (noise)
maxima_filtered = bwareaopen(maxima, 10)

# Label the maxima as markers
markers = label_components(maxima_filtered)

# Impose maxima on negative distance for watershed
D_comp = -D
D_mod = imimposemin(D_comp, maxima_filtered)

# Perform watershed segmentation
L = watershed(D_mod)

# Display results
subplot(1, 3, 1)
imshow(I)
title!("Original")

subplot(1, 3, 2)
imshow(maxima_filtered)
title!("Filtered Maxima")

subplot(1, 3, 3)
imshow(label2rgb(L))
title!("Watershed Segmentation")

showfig()

Detect Peaks in Elevation Data

(These are Claude.ai dreams but maybe worth including)

Use regional maxima to find peaks in a digital elevation model:

# Load elevation data
DEM = gmtread("elevation.tif")

# Find regional maxima (peaks, summits)
peaks = imregionalmax(DEM)

# Remove small spurious maxima
peaks_clean = bwareaopen(peaks, 20)

# Overlay peaks on elevation map
imshow(DEM, cmap=:terrain)
overlay!(peaks_clean, color=:red, alpha=0.8)
colorbar!()
title!("Peaks in Elevation Data")

Pre-process Image with H-Maxima Transform

Suppress shallow maxima before finding regional maxima:

# Load image
I = gmtread("rice.png")

# Original regional maxima (many spurious maxima)
maxima_orig = imregionalmax(I)

# Apply H-maxima transform to suppress shallow maxima
I_hmax = imhmax(I, 10)

# Find regional maxima after suppression
maxima_filtered = imregionalmax(I_hmax)

# Compare results
subplot(1, 3, 1)
imshow(I)
title!("Original")

subplot(1, 3, 2)
imshow(maxima_orig)
title!("Original Maxima ($(sum(maxima_orig)) regions)")

subplot(1, 3, 3)
imshow(maxima_filtered)
title!("Filtered Maxima ($(sum(maxima_filtered)) regions)")

showfig()

Count Number of Regional Maxima

To count the number of regional maxima pixels:

I = gmtread("sample.png")
BW = imregionalmax(I)

# Count maxima pixels
n_pixels = sum(BW)
println("Number of regional maxima pixels: $n_pixels")

# Count maxima regions (connected components)
CC = bwconncomp(BW)
n_regions = CC.NumObjects
println("Number of regional maxima regions: $n_regions")

See Also

imregionalmin, imhmax, watershed, imreconstruct, bwareaopen, bwdist