There is a trend in Computer Vision to use over twenty colour names for image annotation, retrieval and to train deep learning networks to name unknown colours for human use. This paper will show t ...

Digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids. Such methods have been widely used in many medical imaging applications, including image segmentation, visualization, manipulation, interpolation, registration, surface-tracking, object representation, correction, quantitative morphometry etc. Digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability, fidelity, and efficiency. This paper presents a comprehensive yet compact survey on results, principles, and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications. Specifically, this paper reviews methods related to distance analysis and path propagation, connectivity, surface-tracking, image segmentation, boundary and centerline detection, topology preservation and local topological properties, skeletonization, and object representation, correction, and quantitative morphometry. A common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity, path propagation, and neighborhood analysis.

The paper presents a novel procedure to hierarchically decompose a multiscale discrete skeleton. The skeleton is a linear pattern representation that is generally recognized as a good shape descriptor. For discrete images, the discrete skeleton is often preferable. Multiresolution representations are convenient for many image analysis tasks. Our resulting skeleton decomposition shows two different types of hierarchy. The first type of hierarchy is one of different scales, as the original pattern is converted into an AND-pyramid and the skeleton is computed for each resolution level. The second type of hierarchy is established at each level of the pyramid by identifying and ranking skeleton subsets according to their permanence, where permanence is a property intrinsically related to local pattern thickness. To achieve the decomposition, both bottom-up and top-down analysis in the sense of moving from higher to lower resolution and vice versa are used. The bottom-up analysis is used to ensure that a part of the skeleton that is connected at a higher resolution level is also connected (if at all present) in the next, lower resolution level. The top-down analysis is used to build the permanence hierarchy ranking the skeleton components. Our procedure is based on the use of (3/spl times/3) local operations in digital images, so it is fast and easy to implement. This skeleton decomposition procedure is most effective on patterns having different thickness in different regions. A number of examples of decompositions of multiscale skeletons (with and without loops) are shown. The skeletons are, in most cases, nicely decomposed into meaningful parts. The procedure is general and not limited to any specific application.

Most agricultural statistics are calculated per field, and it is well known that classification procedures for homogeneous objects produce better results than per-pixel classification. In this study, a multispectral segmentation method for automated delineation of agricultural field boundaries in remotely sensed images is presented. Edge information from a gradient edge detector is integrated with a segmentation algorithm. The multispectral edge detector uses all available multispectral information by adding the magnitudes and directions of edges derived from edge detection in single bands. The addition is weighted by edge direction, to remove "noise" and to enhance the major direction. The resulting edge from the edge detection algorithm is combined with a segmentation method based on a simple ISODATA algorithm, where the initial centroids are decided by the distances to the edges from the edge detection step. From this procedure, the number of regions will most likely exceed the actual number of fields in the image and merging of regions is performed. By calculating the mean and covariance matrix for pixels of neighboring regions, regions with a high generalized likelihood-ratio test quantity will be merged. In this way, information from several spectral bands (and/or different dates) can be used for delineating field borders with different characteristics. The introduction of the ISODATA classifier compared with a previously used region growing procedure improves the output. Some results are compared with manually extracted field boundaries.

Coarse-to-fine skeletons of digital patterns in binary images are computed on a grey-level pyramid. This is built in such a way that pattern shape and topology are preserved at all resolution levels, as faithfully as possible. A key problem is spurious holes, created at lower resolutions by region merging, that would originate spurious loops in coarse skeletons. This is solved by a novel technique exploiting the grey-level pyramid.

A multiresolution skeletonization algorithm is presented. The underlying data structure is a binary AND-pyramid. Notwithstanding the fact that the AND-pyramid is likely to break pattern connectedness at lower resolution levels, the algorithm generates connected skeletons at all resolution levels. It can most conveniently be implemented on a parallel SIMD architecture, but efficient MIMD and sequential implementations are also possible. A hierarchy among skeleton branches at various resolutions levels is also introduced.

We present an algorithm to build covering polyhedra for digital 3D objects, by iteratively filling local concavities. The resulting covering polyhedron is convex and is a good approximation of the convex hull of the object. The algorithm uses 3x3x3 operators and requires a few minutes for a 128 x 128 x 128 image, when implemented on a sequential computer. Once the covering polyhedron has been obtained, the object concavities can be identified by subtracting the object from the polyhedron and suitably post-processing the set difference. Features characterising the concavities can then be extracted and used as a tool for quantitative shape analysis.

Presents an iterative parallel procedure for computing concavity trees of a digital shape in a multi-resolution structure. The pattern is, at all resolution levels, covered by an almost convex polygon, closely fitting the pattern itself. When the polygons have been created, a hierarchical structure is built, which points out the relations among the concavities at different resolution levels. Also some properties characterizing the added regions are computed. On the highest resolution level, a meta-concavity tree is built up. This tree can be used to analyse and hierarchically rank the shape concavities.>

A parallel algorithm for smoothing and/or decomposing binary digital shapes is presented. The method uses a multiresolution pyramid, making it particularly suitable for parallel pyramid machines. The binary shape is first converted into a resolution pyramid. The lower resolution levels are used to smooth the shape at higher resolution levels. The smoothed versions, at different resolution levels, are then used to decompose the shape. This means that the shape is decomposed into parts according to the local thickness of the shape. The small and the slice-shaped components of the decomposition are finally merged into the larger components.>

An efficient skeletonizing algorithm is presented for the hexagonal grid. The skeleton has unit width, except at crossings and in regions of the shape having even width. Otherwise the skeleton has all the properties generally required for correct skeletons. It includes all local maxima, so complete recovery of the original shape is obtained by using the reverse distance transformation. The algorithm uses only local operations. Thus it can be performed both on sequential and parallel computers. In the sequential case described only three passes through the image are necessary, two to compute the distance transform and one for the identification of skeletal pixels.>

The algorithm matches edges by minimizing a generalized distance between them. The matching is performed in a series of images depicting the same scene with different resolutions, i.e. in a resolution pyramid. Using this hierarchical structure reduces the computational load significantly. The algorithm is reasonably simple to implement and is insensitive to noise and other disturbances. The algorithm has been tested in several applications. Two of them are briefly presented. In the first application the outlines of common tools are matched to gray-level images of the same tools, with overlapping. In the second application lake edges from aerial photographs are matched to lake edges from a map, with translation, rotation, scale, and perspective changes. The hierarchical chamfer matching algorithm gives correct results using a reasonable amount of computational resources in all tested applications.>