AFCMAdaptive (Adaptive Fuzzy C-Means for Image Segmentation) Documentation

🔍 Overview

AFCMAdaptive is an image segmentation algorithm that extends Fuzzy C-Means by introducing a spatially varying multiplier field m(i,j). This adaptive mechanism improves segmentation in images with intensity inhomogeneity such as MRI or CT scans.

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⚙️ Class Definition

Class Name: AFCMAdaptive

This class implements the AFCM algorithm with iterative updates for cluster centers, fuzzy membership, and the multiplier field.

class AFCMAdaptive:
    def __init__(self, n_clusters: int = 3, m: float = 2.0, k1: float = 0.1, k2: float = 0.1,
                 max_iter: int = 100, tol: float = 1e-4):
        ...

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📋 Parameters

Parameter	Type	Default	Description
n_clusters	int	3	Number of segmentation classes
m	float	2.0	Fuzziness degree
k1	float	0.1	First-order regularization weight for multiplier field
k2	float	0.1	Second-order regularization weight for multiplier field
max_iter	int	100	Maximum number of EM iterations
tol	float	1e-4	Convergence tolerance for center updates

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🚀 Usage Examples

from soft_clustering._afcm_adaptive._afcm_adaptive import AFCMAdaptive
import numpy as np

# Sample synthetic image
image = np.zeros((64, 64))
image[:32, :] = 0.3
image[32:, :] = 0.7
image += np.random.normal(0, 0.05, image.shape)

model = AFCMAdaptive(n_clusters=2)
model.fit(image)

labels = model.predict()
membership = model.get_membership()

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📥 Input / 📤 Output

• Input to fit(image):

  • image (np.ndarray): 2D grayscale image with values ∈ [0,1] or scaled

• Returns:

  • predict() → 2D integer array with cluster labels (H x W)

  • get_membership() → 3D array with fuzzy membership values (H x W x C)

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🛠️ Methods

• fit(image): Performs iterative fuzzy clustering on 2D image

• predict(): Returns hard labels for each pixel

• get_membership(): Returns fuzzy membership matrix for each class

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📝 Implementation Notes

• Multiplier field m(i,j) is updated based on local pixel statistics

• Uses Gaussian smoothing and Laplacian (∇m, ∇²m) for regularization

• Memberships updated using a Mahalanobis-like normalized distance

• Avoids hard intensity boundaries by spatial adaptation

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📚 Reference

This implementation is based on:
“An adaptive fuzzy C-means algorithm for image segmentation in the presence of intensity inhomogeneity”