KEYWORDS: Digital watermarking, Image compression, Data corrections, Image quality, Image restoration, Data hiding, Lithium, Quantization, Information security, Steganography
This paper investigates the distortion-free robust watermarking by multiple marking. Robust watermarking
is first performed. Then, by reversible watermarking, the information needed to invert both the robust and
the reversible watermarking is embedded. In case of no attacks, the robust watermark is detected and the
authorized party exactly recovers the original. In case of attacks, one can suppose that the robust watermark
can still be detected, but the reversibility is lost. The approach relies on the embedded capacity of the reversible
watermarking. The overall scheme inherits the robustness of the ?rst marking stage. The selection of the robust
and of the reversible watermarking schemes is discussed. In order to improve the robustness of the first marking
stage against the second one a joint marking procedure is proposed. A case study of reversible watermarking
providing very good robustness against JPEG compression is presented.
KEYWORDS: Digital watermarking, Image restoration, Data hiding, Data compression, Image compression, Lithium, Image storage, Information security, Steganography, Multimedia
This paper continues the researches on a recently proposed reversible watermarking approach based on an integer transform defined for pairs of pixels. The transform is invertible and, besides, for some pairs of pixels, the original values are recovered even if the LSBs of the transformed pixels are overwritten. Two watermarking schemes, a simple one and a modified version, have been developed to embed watermarks into image LSB plane without any other data compression. At detection, original image is exactly recovered by using a simple map which keeps track of the transformed pairs and the LSBs of the unchanged pairs of pixels. The main contribution of this paper is the generalization of the transform for groups of n pixels, where n ⩾ 2. Transforming groups larger than 2 pixels, the size of the map decreases and thus, the hiding capacity of the scheme can increase. In this general context, it appears that the behavior of the transform depends on the parity of n i.e., n even is more appropriate for reversible watermarking. It is also shown that, for n ⩾ 4 the simple scheme and the modified one give very similar data hiding capacity, i.e., the same performance is obtained at a lower computational cost.
KEYWORDS: Digital watermarking, Image restoration, Data hiding, Image encryption, Image compression, Symmetric-key encryption, Data compression, Information operations, Radon, Free space
This paper proposes a low computational reversible watermarking approach. An integer transform is defined for pairs of pixels. The transform is invertible and, besides, for some pairs of pixels, the original values are recovered even if the LSBs of the transformed pixels are overwritten. This allows watermarking embedding into image LSB plane without any other data compression scheme. At detection, original image is exactly recovered. The method is of interest for image authentication and data hiding. Experimental results are provided.
KEYWORDS: Digital watermarking, Visualization, Transform theory, Image segmentation, Bridges, Linear filtering, RGB color model, Image enhancement, Image processing, Digital filtering
This paper presents new results on regional image watermarking by exact histogram specification. Image is split in regions and for each region a watermark is specified. Watermarks are selected such as image original histogram is preserved. Main improvement of proposed regional scheme consists in the marking of the entire image (all the regions) with complementary watermarks. This procedure considerably increases watermarking robustness. The region selection strategy is discussed so that direct identification of regions and bordering effects are eliminated. Robustness/fragility of the proposed scheme depends on the specified histograms. In a general setting, exact histogram specification allows only certain graylevel values for the pixels of each region. Fragile watermarking is obtained when sentinel pixels' region is allowed to take only certain discrete values. Thus, using sparse histograms, one achieves not only image authentication, but also, in case of any attack or malicious editing, the detection of the area where image has been altered. On the contrary, robust watermarking against many attacks is obtained when pixels of each region are allowed to take values on compact intervals of graylevels.
The paper investigates the use of image histograms as watermarks. First, the problem of exact histogram specification is addressed and a method for exact histogram specification, consistent with the human perception of brightness, is developed. Next, two watermarking techniques based on exact histogram specification are proposed. The first one directly considers image histograms as watermarks. Thus, a particular histogram is assigned as a watermark and images are further transformed to have exactly the assigned histogram. Since quite large variations in image histogram are not perceived by humans, an unlimited number of invisible watermarks can be defined for which images appear visually non-distorted. Besides, by selecting histograms which are variations of uniform histogram, the transformed images are not only uniquely marked but also enhanced. The second approach conserves, for each image, its original histogram. The watermarking procedure consists of two histogram specification transforms: a transform to the assigned watermark followed by an inverse transform to recover the original histogram. Since image recovery after a histogram specification transform is not exact, the error obtained after the two consecutive transforms is further used to track each watermark.
On the discrete grid, the alternate use of V4-V8 neighborhoods is known to approximate the Euclidean distance. This problem was analyzed in the continuous setting and, more generally, it was shown that, if a certain inclusion holds for the unit balls of k distances, their alternate use yields a true distance, called sandwich distance. This paper elaborates on this topic. The initial scope is enlarged by defining new families of distances, called mixed distances. They are compositions of linear combinations of distances and of sandwich distances. Two examples of iterations of mixed distances are investigated. Their unit balls are polygons with 2k sides; their convergence towards the Euclidean disk is analyzed.
Many authors, e.g., Rosenfeld and Pfaltz, Borgefors..., have proposed efficient and/or accurate approximations of euclidian distance on a 2D or 3D grid with methods which are connected, more or less directly, to norm derived distances, e.g., with Lp norms. This paper enlarges the scope in a continuous and m-dimensional framework. It presents a new broad class of distances, called 'sandwich' or 'periodic' distances. They are obtained by compounding in a periodic manner a certain number of norm-derived distances. The main result of this paper is the proof of a sufficient condition under which the triangular inequality is fulfilled, i.e., that the unit balls of the compounded distances belong to an ascending chain. Moreover, the theory includes weighted distances, giving this tool a high degree of flexibility.
The paper addresses the problem of finding fast algorithms that accurately generate arbitrary curves on discrete lattices. The curves are supposed to have certain smoothness. No special assumption is made on their given representation (e.g. parametric, nonparametric, tabular). The proposed method consists of two stages, namely learning and drawing. In the learning stage, each curve is piecewise approximated by polynomials and then algorithms for generating the polynomials are derived. The algorithms are similar to those developed by Bresenham for straight lines and circular arcs. They are based on an integer decision variable and on an updating procedure. The decision process minimizes the error between the ideal curve and the digital one. The updating acts as an adaptive rounding off process that prevents the accumulation of errors. The drawing stage is very fast. Neither multiplies nor fractional integer operations are required. The entire curve is piecewise traced. The decision variable is initialized for each polynomial. Each new point is selected from two possible candidates, according to the sign of the decision variable. Two examples, the generation of a circular arc and of a sine-wave, are shown.
KEYWORDS: Image processing, Surface plasmons, Associative arrays, Raster graphics, Digital signal processing, Signal processing, Digital image processing, Data conversion, Silicon, Berkelium
Some signal processing applications require memory modules with very fast access along predefined scan patterns. If this requirement only holds for standard raster scan (image processing) the simple solution of reading in parallel a number of slower memory chips and using a fast parallel to serial converter is enough. This paper focuses on the problems which appear when more different fast scans patterns are required. In this case the mapping of the data in the memory chips is analyzed by using a combinatorial theory setting. We prove that a mapping which allows two different predefined scan patterns does always exist. For more than two different predefined scans our formalism allows one to construct a mapping, if it does exist. The paper presents several examples with 2 and 4 scan patterns.
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