MATLAB Code Implementation for Image Variance and Statistical Features

In digital image processing, statistical features such as variance, skewness, kurtosis, energy, and entropy are commonly used to describe image texture and distribution characteristics. These features help analyze image contrast, pixel value distribution patterns, and other important properties. Variance measures the dispersion of image pixel values, reflecting the image contrast. The calculation method involves computing the average of squared differences between each pixel value and the mean. Higher variance indicates greater image contrast. In MATLAB implementation, the variance of an image matrix can be directly computed using the var function applied to the flattened pixel array: variance_value = var(image_matrix(:)). Skewness describes the asymmetry direction of pixel value distribution. Positive skewness indicates a longer right tail in the distribution, while negative skewness shows the opposite pattern. Calculated using the third central moment, it reveals distribution asymmetry. MATLAB's built-in skewness function efficiently computes this: skewness_value = skewness(image_matrix(:)). Kurtosis reflects the peakedness or flatness of pixel value distribution. High kurtosis means the distribution is more concentrated, while low kurtosis indicates a more dispersed distribution. Based on the fourth central moment calculation, it's often compared with normal distribution. The MATLAB implementation uses: kurtosis_value = kurtosis(image_matrix(:)). Energy represents the sum of squared pixel values, reflecting image uniformity. High energy indicates concentrated pixel value distribution, commonly found in single-tone regions. This can be computed using: energy_value = sum(image_matrix(:).^2). Entropy measures the information content or complexity of an image. Calculated based on probability distribution, higher entropy values indicate more complex textures, while lower values suggest more uniform patterns. MATLAB implementation requires creating a probability distribution from the histogram: [counts, ~] = histcounts(image_matrix(:)); probabilities = counts/sum(counts); entropy_value = -sum(probabilities.*log2(probabilities)). For implementation, MATLAB's built-in functions like var, skewness, and kurtosis can be directly applied to vectorized image data, while entropy calculation requires additional handling of grayscale level probability distribution. These features are widely used in medical imaging, remote sensing analysis, and other fields, providing fundamental data for subsequent classification or detection tasks.