Image Grayscale Statistical Features

In this computational imaging task, we perform statistical analysis on an input image. Specifically, we calculate four fundamental statistical measures: mean, variance, skewness, and kurtosis, which provide crucial insights into the image's characteristics and properties. The mean represents the average pixel intensity value across the entire image, typically computed by summing all pixel values and dividing by the total number of pixels. In implementation, this can be efficiently calculated using functions like mean() in MATLAB or numpy.mean() in Python. Variance quantifies the dispersion of pixel values around the mean, calculated as the average of squared differences between each pixel value and the mean. This measure indicates the image's contrast level and can be implemented using var() in MATLAB or numpy.var() in Python. Skewness measures the asymmetry of the pixel value distribution. A positive skew indicates a concentration of darker pixels with a tail toward brighter values, while negative skew suggests the opposite. Statistical packages like scipy.stats.skew() in Python or the moment() function in MATLAB can compute this parameter. Kurtosis characterizes the "tailedness" and peak sharpness of the distribution compared to a normal distribution. High kurtosis indicates heavy tails and sharp peaks, often seen in images with extreme contrast variations. Implementation typically uses scipy.stats.kurtosis() in Python or specialized statistical toolboxes in MATLAB. By computing these statistical measures, we gain deeper insights into image properties such as brightness distribution, contrast characteristics, and overall tonal distribution patterns, enabling more sophisticated image analysis and processing applications.