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In this article, an optical image encryption algorithm based on chaotic baker’s map is presented. The stego-image is encrypted with the help of double random phase encoding algorithm and then produced disorder with the help of chaotic transformation. Security test shows that the reading of proposed algorithm is very close to the optimal values.

We present a computationally simple and inexpensive method to induce coincidence between one map and another, regardless of their respective projections. We imagine the map to be transformed on a rubber sheet stretched to coincide with a stable base map at an average of 15 control points; for more precise coincidence, we add more control points. We compute triangles on the rubber-sheet map, using control points as vertices, and with a procedure called piecewise linear homeomorphism, map these triangles linearly onto corresponding triangles on the stable map.

Mathematical models can produce desired dynamics and statistical properties with the insertion of suitable nonlinear terms, while energy characteristics are crucial for practical application because any hardware realizations of nonlinear systems are relative to energy flow. The involvement of memristive terms relative to memristors enables multistability and initial-dependent property in memristive systems. In this study, two kinds of memristors are used to couple a capacitor or an inductor, along with a nonlinear resistor, to build different neural circuits. The corresponding circuit equations are derived to develop two different types of memristive oscillators, which are further converted into two kinds of memristive maps after linear transformation. The Hamilton energy function for memristive oscillators is obtained by applying the Helmholz theorem or by mapping from the field energy of the memristive circuits. The Hamilton energy functions for both memristive maps are obtained by replacing the gains and discrete variables for the memristive oscillator with the corresponding parameters and variables. The two memristive maps have rich dynamic behaviors including coherence resonance under noisy excitation, and an adaptive growth law for parameters is presented to express the self-adaptive property of the memristive maps. A digital signal process (DSP) platform is used to verify these results. Our scheme will provide a theoretical basis and experimental guidance for oscillator-to-map transformation and discrete map-energy calculation.

The following article discusses current trends in digital methods used in historical cartographic source editing. Maps are often used not only by scholars interested in spatial history, but also by the general public. Due to increasing popularity of ‘maps online’, it is crucial to discuss, evaluate and classify current solutions and applications used in cartographic source editing. In the article the ‘edition’ is understood as the ‘critical representation of a historical documents’, and many types of map editions are considered. The level of map transformation: from raw image, through georeferenced map to spatial database constitutes the main axis of the division between various types of editions. On the very basic level (maps as images: digital libraries and collections), we only have a raster representation of a historic map, often supplemented by bibliographic metadata and the possibility to download it. The second level is geoportals with georeferenced maps, i.e. with spatial adjustment to modern geographic coordinates. The third, most complex level, includes elaboration of the spatial database with most important features (e.g. settlements, roads, land cover, etc.), which serves as the geographic index. The higher the map transformation level, the more useful the edition becomes. Nevertheless, more complex methods in map processing also should include more documentation about this process which is not always present within discussed projects. The main result of the article, apart from classifying existing applications and proposing their general types is to identify functionality and components of the so-called model edition of a historic map.

Stereo vision is one of the advancements in computer vision and pattern recognition applications using a dual camera to mimic human visuals. This study focused on RGB-depth (RGB-d) map image formation selection parameters, specifically from the stereo image captured on the cili-padi (birds-eye chilli) plant. The process starts from calibrating the camera used with a checkerboard image to obtain the camera's intrinsic and extrinsic resolution. The stereo images were rectified to facilitate the disparity computation between the left and right images. Then, point cloud plotting is acquired by using a triangulation function on the image disparity with the camera parameter value. RGB-d images are computed by normalising the depth information of each point plot into greyscale value or any other suitable colourmap. Comparing the different types of disparity map transformation function algorithms used to produce the RGB-d image shows that using SGM-function provides the best output of RGB-d image formation.

ABSTRACTIn human computer interaction, proxemics describes the ways that people use space to interact with other people or objects. We focus on proxemic maps, which are virtual maps in immersive environments that react to proxemic interaction. Proxemic maps take advantage of new opportunities brought about by immersive visualization, where virtual maps can be freely positioned in virtual or physical space and adapt themselves relative to the spatial position of the viewer. We discuss proxemic interactions that alter the content and type of maps, including changing scale, symbolization, type of visualization and geometry. We propose a novel transformation that changes the geometry of maps based on their proximity to users. Users move the map back and forth and the map transitions between ring, horizontal, vertical and cylindrical geometries. The ring geometry surrounds the user and aligns features on the map with features in the real world. We implemented the map transformation in virtual reality and conducted a user study to evaluate it. The results of the user study indicate that participants preferred the ring and horizontal geometries. The ring geometry is useful because it simplifies connecting virtual features on the map with real features in the landscape, while the horizontal geometry provides an overall view of the landscape. We further found that combination of different geometries helped the study participants to overcome the limitations of each geometry.

ABSTRACTThe adaptive composite map projection technique changes the projection to minimize distortion for the geographic area shown on a map. This article improves the transition between the Lambert azimuthal projection and the transverse equal-area cylindrical projection that are used by adaptive composite projections for portrait-format maps. Originally, a transverse Albers conic projection was suggested for transforming between these two projections, resulting in graticules that are not symmetric relative to the central meridian. We propose the alternative transverse Wagner transformation between the two projections and provide equations and parameters for the transition. The suggested technique results in a graticule that is symmetric relative to the central meridian, and a map transformation that is visually continuous with changing map scale.

A map transformation is a willful geometrical distortion of an image. Examples are rotation, shearing, and local stretching of the coordinate system. We describe an optical setup that performs a map transformation by spatial filtering with two phase-only filters. The system is able to perform in x- and y-linear distortions (e.g., shears) as well as certain x- and y-nonlinear distortions. The distorting filters introduce no aberrations. The object may radiate coherently, incoherently, or partially coherently. Some experimental results are presented.

ABSTRACTFor the representation of geographic information, the distortion resulting from map projections and transformations is unwanted but unavoidable. Identical circles systematically arranged on the Earth's ellipsoid have been extensively used to symbolize the map distortion. Despite their effectiveness and popularity, these circles are not explicitly associated with any specific polygons in the map, thus possibly impairing their relevance if the map-readers are interested in particular regions. More importantly, for the map transformation specifically targeting polygons such as the area cartogram, placing the circles completely within the polygons becomes necessary because two neighboring polygons in an area cartogram could have distinctive distortion characteristics. This paper proposes new computer algorithms to enable a map-distortion symbolization approach based on inscribed circles entirely contained in polygons either on a projected 2D plane or on the Earth's ellipsoid. These inscribed circles in polygons (ICIP) are rendered as a series of maximum or equal-sized circles that are spatially exclusive, that is, without overlapping. Compared with the systematically arranged identical circles, the ICIP give cartographers certain flexibility and a new option for the map-distortion symbolization. Two area cartograms and three map projections are provided as examples to illustrate their usage and possible contribution in different mapping scenarios.

In Turkey, cadastral work began during the Ottoman Empire. There are several kinds of cadastral maps created by different production methods, coordinate system, base type, measurement, and calculation methods. These maps must be transformed into the Turkish national coordinate systems. Although there are many coordinate transformation methods, the affine transformation method is most commonly used in map transformation. The affine transformation solution consists of the adjustment of the obtained unique and best suitable parameters estimation. Although the least square (LS) adjustment method is in widespread use, there are some disadvantages in the determination of erroneous measurements. The least absolute value (LAV) determines the erroneous measurements and their effects on the other measurements results. In recent years, the total least square (TLS) method has been frequently used for estimation parameters. This study examines the transformation of non-digital cadastral maps in Turkey. After the evaluation of the current situation of cadastral maps, the affine transformation method is explained using adjustment methods. Finally, the success of affine transformation combined with the LS, LAV, and TLS methods is demonstrated by a numerical application. Thus, the most suitable adjustment method is obtained according to the results of the application.

Abstract: Purpose: Quantitative assessment and essentially segmentation of liver and its tumours are of clinical importance in various procedures such as diagnosis, treatment planning, and monitoring. Moreover, segmentation of liver is the basis of further processing such as visualization, liver resection planning, and liver shape analysis. In this paper, we propose an algorithm to estimate an initial liver boundary. Methods: The proposed method consists of four steps as follows: first, we compute statistical parameters of liver’s intensity range, associated with a large cross-section of liver CT image, utilizing expectation maximization (EM) algorithm. Second, by automatic extraction of ribs and segmentation of the heart, we define a ROI to confine the liver region for the next operations. Third, we propose a double thresholding approach to divide the liver intensity range into two overlapping ranges. In this case, based on a decision table, we label an object as a liver candidate or disregard it from the rest of the procedures. Finally, we employ an anatomical based rule to finalize a candidate as a liver tissue. In this case, we propose a color-map transformation scheme to convert the liver gray images into color images. In this way, we attempt to visually differentiate the liver from its surrounding tissues. Results: We have evaluated the techniques in the presence of 14 randomly selected local datasets as well as all datasets from the MICCAI 2007 Grand Challenge workshop database. For the local datasets, the average overlap error and average volume difference were of values of 15.3 and 2.8%, respectively. In the case of the MICCAI datasets, the above values were estimated as 20.3 and −4.5%, respectively. Conclusion: The results reveal that the proposed technique is feasible to perform consistent initial liver borders. The boundary might be then employed in an ‘Active Contour’ algorithm to finalize the liver mask.

In the primary somatosensory cortex (SI), the body surface is mapped in a relatively continuous fashion, with adjacent body regions represented in adjacent cortical domains. In contrast, somatosensory maps found in regions of the cerebellar hemispheres, which are influenced by the SI through a monosynaptic link in the pontine nuclei, are discontinuous (“fractured”) in organization. To elucidate this map transformation, the authors studied the organization of the first link in the SI‐cerebellar pathway, the SI‐pontine projection. After injecting anterograde axonal tracers into electrophysiologically defined parts of the SI, three‐dimensional reconstruction and computer‐graphic visualization techniques were used to analyze the spatial distribution of labeled fibers. Several target regions in the pontine nuclei were identified for each major body representation. The labeled axons formed sharply delineated clusters that were distributed in an inside‐out, shell‐like fashion. Upper lip and other perioral representations were located in a central core, whereas extremity and trunk representations were found more externally. The multiple clusters suggest that the pontine nuclei contain several representations of the SI map. Within each representation, the spatial relationships of the SI map are largely preserved. This corticopontine projection pattern is compatible with recently proposed principles for the establishment of subcortical topographic patterns during development. The largely preserved spatial relationships in the pontine somatotopic map also suggest that the transformation from an organized topography in SI to a fractured map in the cerebellum takes place primarily in the mossy fiber pontocerebellar projection. J. Comp. Neurol. 422:246–266, 2000. © 2000 Wiley‐Liss, Inc.

Cartograms are proving increasingly popular, but relatively little is known about the problems related to their use. A test program measured the performance of relatively inexperienced map users in identifying locations on a topological cartogram and on the geographic map from which it was derived. The spatial pattern of errors and the variation in task difficulty showed the dominant influence of two map transformation characteristics: change in angular location with respect to other units and change in unit shape. Also, it took significantly longer to perform the task on the map than on the cartogram.

A computationally efficient piecewise-linear rubber-sheet map transformation is derived by analyzing geometrical relationships of areas, linear equations and inequalities, and simplicial coordinates. The use of simplicial coordinates permits a representation of the rubber-sheet transformation, which is completely independent of the image points. The geometric analysis used in deriving the simplicial coordinates leads to special point-in-polygon algorithms for the rubber-sheeting, which may be employed in more general situations. The geometric analysis also leads to convenient formulas for areas of triangulated regions.

This paper examines spatial search behavior related to intra-urban migration. Its approach is to draw upon related studies to derive expectations with regard to search patterns, and to test these through empirical analysis. This involves identifying and measuring distance, directional, and sectoral spatial biases, for which an algorithm is presented that employs a map transformation and standard ellipse analysis.