Differential area profiles (DAPs) are point-based multiscale descriptors used in pattern analysis and image segmentation. They are defined through sets of size-based connected morphological filters that constitute a joint area opening top-hat and area closing bottom-hat scale-space of the input image. The work presented in this paper explores the properties of this image decomposition through sets of area zones. An area zone defines a single plane of the DAP vector field and contains all the peak components of the input image, whose size is between the zone's attribute extrema. Area zones can be computed efficiently from hierarchical image representation structures, in a way similar to regular attribute filters. Operations on the DAP vector field can then be computed without the need for exporting it first, and an example with the leveling-like convex/concave segmentation scheme is given. This is referred to as the one-pass method and it is demonstrated on the Max-Tree structure. Its computational performance is tested and compared against conventional means for computing differential profiles, relying on iterative application of area openings and closings. Applications making use of the area zone decomposition are demonstrated in problems related to remote sensing and medical image analysis.

In this paper we present a fast, interactive method for collecting structural primitives from objects of interest contained within manually selected image regions. The input image is projected onto a Max-Tree and Min-Tree structure from which a pixel-to-node mapper marks the nodes of each tree that correspond to peak components explicitly contained within the selected window. In a pass through the selected nodes, an attribute vector is constructed from the pool of auxiliary data associated with each node separately. The set of all attribute vectors is mapped into a pre-computed multidimensional feature space from which a binary criterion is constructed to accept or reject the remaining image objects. The method is demonstrated in a real application on information extraction from very high resolution satellite imagery.

In this paper, we present a new method for attribute filtering, combining contrast and structural information. Using hyperconnectivity based on k-flat zones, we improve the ability of attribute filters to retain internal details in detected objects. Simultaneously, we improve the suppression of small, unwanted detail in the background. We extend the theory of attribute filters to hyperconnectivity and provide a fast algorithm to implement the new method. The new version is only marginally slower than the standard Max-Tree algorithm for connected attribute filters, and linear in the number of pixels or voxels. It is two orders of magnitude faster than anisotropic diffusion. The method is implemented in the form of a filtering rule suitable for handling both increasing (size) and nonincreasing (shape) attributes. We test this new framework on nonincreasing shape filters on both 2D images from astronomy, document processing, and microscopy, and 3D CT scans, and show increased robustness to noise while maintaining the advantages of previous methods.

In this paper a new feature descriptor, the differential area profile (DAP), is presented. DAPs, like the regular differential morphological profiles, are computed from some size distribution. The proposed method is based on the area metric given by regular connected area filters. Area compared to local width, i.e. the diameter of the structuring element in the corresponding set of openings by reconstruction in classical DMPs, leads to a rather different multi-scale decomposition. This is investigated here and an example on a very high resolution satellite image tile is given.

In medical imaging, anatomical and other structures such as urinary stones, are often extracted with the aid of active contour/ surface models. Active surface-based methods have robustness limitations and are computationally expensive. In this paper we present a morphological method based on attribute filters and the newly presented sphericity attribute. The operators involved, extract the targeted objects in their entirety without shape/size distortions and proceed rapidly. Experiments on three real 3D data-sets demonstrate their efficiency and their performance is discussed.

Connected filters are edge-preserving morphological operators, which rely on a notion of connectivity. This is usually the standard 4 and 8-connectivity, which is often too rigid since it cannot model generalized groupings such as object clusters or partitions. In the set-theoretical framework of connectivity, these groupings are modeled by the more general second-generation connectivity. In this paper, we present both an extension of this theory, and provide an efficient algorithm based on the Max-Tree to compute attribute filters based on these connectivities. We first look into the drawbacks of the existing framework that separates clustering and partitioning and is directly dependent on the properties of a preselected operator. We then propose a new type of second-generation connectivity termed mask-based connectivity which eliminates all previous dependencies and extends the ways the image domain can be connected. A previously developed Dual-Input Max-Tree algorithm for area openings is adapted for the wider class of attribute filters on images characterized by second-generation connectivity. CPU-times for the new algorithm are comparable to the original algorithm, typically deviating less than 10 percent either way.

A new theoretical development is presented for handling the over-segmentation problem in partitioning-based connected openings. The definition we propose treats singletons generated with the earlier method, as elements of a larger connected component. Unlike the existing formalism, this new method allows detection of filamentous structures linking larger objects. This is demonstrated in attribute filtering on neuron images.