This paper proposes a method for fast construction of the entropy field calculated in a sliding local window. The method is based on the representation of the local histogram by a truncated series using cosine basis functions and approximation of the entropy value using regression models. Experiments show a gain in time compared to the direct calculation of the entropy field with a good enough quality of approximation. The method can be applied for other histogram features calculation (e.g., rank statistics). It is reasonable to use the proposed method for obtaining additional features when analyzing large size remote sensing images, where the processing speed is critical.