A new combinatoria characterization of a gray-tone image called Euler Vector is proposed. Euler number of a binary image is a well-known topological feature, which remains invariant under translation, rotation, scaling, and rubber-sheet transformation of the image. Euler vector comprises of a 4-tuple, where each element is an integer representing the Euler number of the partial binary image formed by the four most significant bit planes of the gray-tone image.Experimental results demonstrate robustness of Euler vector under compression and inclusion of noise followed by filtering. The vector is topologically invariant and can be used for image indexing and retrieval.