An efficient algorithm is presented for the computation of grayscale morphological operations with arbitrary 2-D flat structuring elements (S.E.). The required computing time is independent of the image content and of the number of gray levels used. It always outperforms the only existing comparable method, which was proposed in the work by Van Droogenbroeck and Talbot, by a factor between 3.5 and 35.1, depending on the image type and shape of S.E. So far, filtering using multiple S.E.s is always done by performing the operator for each size and shape of the S.E. separately. With our method, filtering with multiple S.E.s can be performed by a single operator for a slightly reduced computational cost per size or shape, which makes this method more suitable for use in granulometries, dilation-erosion scale spaces, and template matching using the hit-or-miss transform. The discussion focuses on erosions and dilations, from which other transformations can be derived.

In this paper, we describe a multiscale and multishape morphological method for pattern-based analysis and classification of gray-scale images using connected operators. Compared with existing methods, which use structuring elements, our method has three advantages. First, in our method, the time needed for computing pattern spectra does not depend on the number of scales or shapes used, i.e., the computation time is independent of the dimensions of the pattern spectrum. Second, size and strict shape attributes can be computed, which we use for the construction of joint 2D shape-size pattern spectra. Third, our method is significantly less sensitive to noise and is rotation-invariant. Although rotation invariance can also be approximated by methods using structuring elements at different angles, this tends to be computationally intensive. The classification performance of these methods is discussed using four image sets: Brodatz, COIL-20, COIL-100, and diatoms. The new method obtains better or equal classification performance to the best competitor with a 5 to 9-fold speed gain.

An efficient algorithm is presented for the computation of gray-scale morphological operations with 2-D structuring elements (S.E.). The required computing time is independent of the image content and of the number of gray levels used. For circular S.E.s, it always outperforms the only existing comparable method, which was proposed by Van Droogenbroeck and Talbot (1996), by a factor between 1.8 and 8.6, depending on the image type. So far, filtering using multiple S.E.s is always done by performing the operator for each size and shape of the S.E. separately. With our method filtering with multiple S.E.s can be performed by a single operator for a reduced computational cost per size or shape, which makes this method more suitable for use in granulometries, dilation-erosion scale spaces, and template matching using the hit-or-miss transform.