Erik R. Urbach

Connected Shape-Size Pattern Spectra for Rotation and Scale-Invariant Classification of Gray-Scale Images

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

Efficient 2-D Grayscale Morphological Transformations With Arbitrary Flat Structuring Elements

An efficient algorithm is presented for the computation of grayscale morphological operations with arbitrary 2D 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.

Vector-Attribute Filters

A variant of morphological attribute filters is developed, in which the attribute on which filtering is based, is no longer a scalar, as is usual, but a vector. This leads to new granulometries and associated pattern spectra. When the vector-attribute used is a shape descriptor, the resulting granulometries filter an image based on a shape or shape family instead of one or more scalar values.

Connected rotation-invariant size-shape granulometries

In this paper, we describe a rotation-invariant multi-scale morphological method for texture analysis. Compared with the existing methods, our method has three advantages. First, it can be implemented efficiently. Furthermore, our method can be used for the computation of size and strict shape attributes, which we use for the computation of 2-D size-shape pattern spectra. Finally, our method is rotation-invariant. Although the latter can also be approximated by morphological methods by using structuring elements at different angles, this tends to be computationally intensive.

Segmentation of cracks in shale rock

In this paper the use of morphological connected filters are studied for segmenting sheet- and thread-like cracks in images of shale rock. A volume formed from a stack of 2-D X-ray images is processed using 3-D attributes. The shape-preserving property of these filters provides accurate segmentation results while the use of rotation-invariant attributes allow robust and computationally efficient segmentation of cracks at all orientations. The results obtained using shape and size attributes are provided and discussed. The research presented here is part of a project with geologists to provide tools for automated segmentation and analysis of features of interest in various types of rock.

Contextual image filtering

A morphological attribute filter uses a criterion to decide which connected components to preserve and which to remove. So far, these criteria considered only attributes of each component individually. In this paper, a new type of attribute filter is proposed, where context attributes of a component are considered. These context attributes describe how that component relates to other components in the image. Alignment, distance, and similarities in size, shape, and orientation between the individual components can be used to determine which components belong to the same context. The resulting contextual filter can be used to preserve only those components which visually appear to belong to a certain group of similar components. It can be used to detect textures or patterns of connected components. Although similar results could be obtained by applying a dedicated series of conventional filters, the proposed algorithm requires at most a redefinition of some rules instead of the elaborate design and implementation of a complete new method.

Efficient 2-D Gray-Scale Dilations and Erosions with Arbitrary Flat Structuring Elements

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.

Connected morphological operators improve image classification

A new method of pattern-based analysis increases speed and accuracy and is invariant to image orientation.