Abstract <p>Smoothing is one of the most common operations in video processing. Many different approaches to solving this problem are known, but the reason why some algorithms perform better results than others has not been fully understood. Research shows that one of the most important issues in constructing a smoothing algorithm is the correct localization of the evaluation area, i.e., the set of points that participate in determining the value of the target point. The difference between local analysis methods that use an evaluation area of constant shape or a variable shape adapted to a specific processed signal is demonstrated. Selection of the desired evaluation area is based on the interpretation of the image as a piecewise smooth surface in the coordinate-brightness space. A comparison of smoothing algorithms using different approaches is carried out.</p>