The paper presents a comparative study of several algorithms developed for digital image rotation. No losing generality we studied gray scale images. We have tested methods preserving gray values of the original images, performing some interpolation and two procedures implemented into the Corel Photo-paint and Adobe Photoshop soft packages. By the similar way methods for rotation of color images may be evaluated also.
A continuous figure may be represented by a binary image on a discrete grid. Continuous figures possess some invariant properties with respect to translation, rotation and symmetry. In the paper we evaluate maximal and relative errors of several invariant features based on central moments calculated for various geometric figures in 1D and 2D digital spaces.
In computer science there ha been increasing interest in development of matching measures for gray scale images. This problem has lots of applications from pure image matching to image retrieving from an image data base. There are various strategies and approaches to image comparison. In the paper we summarize many of them and give a short overview. Various types of low-level measures are studied and their properties are described. We show that measures based on our idea presented in 'vision geometry-95' is the best choice for the low-level image matching SOme new properties of this measure are explored. Several applications for matching strategy based on the measure are given.
A new class of functions is studied. They are generalizations of the little-known `flower-shop distance'. We call them touching functions. Some of them are metrics, i.e. touching metrics (TM). Disks, circles and digital paths based on these metrics are also studied. The distance transform based on TMs is introduced and a scheme for the algorithm is given.
There are papers describing measures of correspondence or similarity between two binary images or their parts, but only two papers suggest a measure for a comparison of objects of two grey-scale images. However, there are numerous applications of a measure for grey-scale images as whole entities. A useful application is the comparison of different algorithms devoted to the same task (edge detection, thresholding, image enhancement, segmentation and image reconstruction). This paper proposes some results to define such a measure. They are based on two different representations of grey-scale images: as `surfaces' and as `stacks' or umbra. We study an adaptation of some known formulas used for binary images to grey-scale images, and present a geometrical variant of such a measurement. We study different measures of diversity, based on different digital metrics, direct calculations of distances, and digital functions adapted to grey-scale images. We show that the `stack' representation needs more calculation time and that measures based on the representation are not sensitive to small image shifts, but very sensitive to noise.
Digital mathematical morphology (MM) and the distance transform (DT) have many points of intersection. The DT combines numerical features and object shapes. Usual application of mathematical morphology uses distance transforms based on the trivial city-block or chessboard metrics like digital representation of continuous ball. In this paper we concern structuring element as oriented neighborhood structures (ONSs) defined in the digital space; wider class of digital metrics and nonmetric functions defined on these NSs. We show that basic morphological operations may be performed by a thresholding of results of local propagations based on this class of digital functions. Such approach simplifies a description of some structuring elements and some operations of image analysis.
The construction of filters or filter operators is an important problem in image processing. In this paper it is described how one can construct a filter operator based on the Distance Transformation for grey-scale image. This operator is similar to max/min filters for grey-scale images. We call this operator quasi-median filter. It is not a filter from the morphological point of view like median filter, but it posses filter (mean) properties.
The structure extraction task is analyzed. The co-occurrence matrices (CMs) are the popular basis for this goal. We show that binary preparation of arbitrary texture preserves its structure. This transformation decreases the computation time of analysis and the required memory in dozens times. A number of features for detecting displacement vectors on binarized images are compared. We suggest to use CM elements jointly as the united feature for this goal. We have shown that it is a stable detector for noisy images and simpler than well- known (chi) 2 and (kappa) statistics.
The digital Mathematical Morphology and the Distance Transform (DT) have many points of intersection. The DT combines numerical features and objects shapes. The properties of digital distance functions (metrics, asymmetries and quasi-metrics) and DT based on these functions are studied. Some extensions of the transform and the interpretation of the grey scale DT by application of the binary DT in the n-dimensional digital space are given. The morphological erosion and dilation may be performed by the DT for binary and grey scale images.
This paper develops some aspects of a structural texture design. We combine continuous and digital geometrical primitives with digital images. A structural textured image is represented as a finite set of texture elements (TEs) and placement rules which govern the spatial relation between them. 1D or 2D geometrical primitives in the Euclidean plane are utilized. The primitive is a domain of a tone function F of 1D and 2D texture elements TEs. We consider the design of different texture pictures: (1) simple structural texture (with one TE), (2) structural textures with nonlinear placement rules, (3) structural textures with few TEs, (4) noised texture, (5) linear textured image. These models allow to synthesize different textured images which have a structural nature.
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