imregionalmin

Regional minima

Description

BW = imregionalmin(I)

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

BW = imregionalmin(I, conn)

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

Data Types: Bool

Examples

Find Regional Minima in Simple Array

Create a simple sample array with several regional minima:

A = 10 * ones(10, 10)
A[2:4, 2:4] .= 3
A[6:8, 6:8] .= 8

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   3.0   3.0   3.0  10.0  10.0  10.0  10.0  10.0  10.0
 10.0   3.0   3.0   3.0  10.0  10.0  10.0  10.0  10.0  10.0
 10.0   3.0   3.0   3.0  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   8.0   8.0   8.0  10.0  10.0
 10.0  10.0  10.0  10.0  10.0   8.0   8.0   8.0  10.0  10.0
 10.0  10.0  10.0  10.0  10.0   8.0   8.0   8.0  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 minima. 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 minima. imregionalmin sets all other pixels to false (or 0):

regmin = imregionalmin(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  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  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

Find Regional Minima in Grayscale Image

Load a grayscale image:

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

Find the regional minima:

BW = imregionalmin(I)
imshow(BW)

Overlay the regional minima on the original image:

# Create an overlay showing minima in red
imshow(I)
# Mark regional minima
overlay!(BW, color=:red)

Compare Different Connectivity Settings

Create a test image with a saddle point:

# Create an image with a valley structure
I = zeros(15, 15)
I[8, :] .= 5  # Horizontal ridge
I[:, 8] .= 5  # Vertical ridge
I[8, 8] = 3   # Saddle point

Compute regional minima with different connectivity:

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

# 8-connectivity (edges and corners)
BW8 = imregionalmin(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()

Detect Valleys in Elevation Data

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

Use regional minima to find valleys in a digital elevation model:

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

# Find regional minima (valleys, depressions)
valleys = imregionalmin(DEM)

# Remove small spurious minima
valleys_clean = bwareaopen(valleys, 50)

# Overlay valleys on elevation map
imshow(DEM, cmap=:terrain)
overlay!(valleys_clean, color=:blue, alpha=0.7)
colorbar!()
title!("Valleys in Elevation Data")

Pre-process Image with H-Minima Transform

Suppress shallow minima before finding regional minima:

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

# Original regional minima (many spurious minima)
minima_orig = imregionalmin(I)

# Apply H-minima transform to suppress shallow minima
I_hmin = imhmin(I, 10)

# Find regional minima after suppression
minima_filtered = imregionalmin(I_hmin)

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

subplot(1, 3, 2)
imshow(minima_orig)
title!("Original Minima ($(sum(minima_orig)) regions)")

subplot(1, 3, 3)
imshow(minima_filtered)
title!("Filtered Minima ($(sum(minima_filtered)) regions)")

showfig()

Notes

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

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

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

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

Tips

• Use imhmin to suppress shallow regional minima before detection

• Apply bwareaopen to remove small spurious regional minima

• Combine with watershed for marker-based image segmentation

• For elevation data, regional minima identify valleys, sinks, and depressions

• Use imimposemin to force specific minima before watershed segmentation

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

See Also

imregionalmax, imhmin, watershed, imreconstruct, bwareaopen