We introduce three generalizations of homotopy equivalence in digital images, to allow us to express whether a finite and an infinite digital image are similar with respect to homotopy. We show that these three generalizations are not equivalent to ordinary homotopy equivalence, and give several examples. We show that, like homotopy equivalence, our three generalizations imply isomorphism of fu...

There is a general consensus on the fact that people love food. Due to the great diffusion of low cost image acquisition devices (e.g., smartphones and wearable cameras), the food is nowadays one of the most photographed objects. The number of food images on the web is increasing and novel social networks for food lovers (e.g., foodspotting) are more and more popular. The automatic analysis and...

The geometrical transformations change the spatial relationship between objects in an image. One of the principle applications of geometric transformations concerns the possibility of correcting the digital images of the distortions introduced by the camera. Often the images produced by inexpensive cameras present geometric distortions of a very large nature. These images must be corrected in o...

The growth of networked multimedia systems has magnified the need for image copyright protection. One approach used to address this problem is to add an invisible structure to an image that can be used to seal or mark it. These structures are known as digital watermarks. In this paper we describe two techniques for the invisible marking of images. We analyze the robustness of the watermarks wit...

The degree of imperceptibility of hidden image in the ‘Digital Image Steganography’ is mostly defined in relation to the limitation of Human Visual System (HVS), its chances of detection using statistical methods and its capacity to hide maximum information inside its body. Whereas, a tradeoff does exist between data hiding capacity of the cover image and robustness of underlying information hi...

We present a domain-independent ICA-based approach to watermarking. This approach can be used on images, music or video to embed either a robust or fragile watermark. In the case of robust watermarking, the method shows high information rate and robustness against malicious and nonmalicious attacks, while keeping a low induced distortion. The fragile watermarking scheme, on the other hand, show...

The valence of any visual paradigm and its accompanying technologies is subject to the contingencies of political regimes and cultural shifts. The instigation, implementation and even reconfiguring of any associated technological system effects a translation and adjustment to the structure and use of these supporting mechanisms that both re-defines the relationship between object and viewer and...

A distance transformation converts a binary digital image, consisting of feature and non-feature pixels, into an image where all non-feature pixels have a value corresponding to the distance to the nearest feature pixel. Computing these distances is in principle a global operation. However, global operations are prohibitively costly. Therefore algorithms that consider only small neighborhoods, ...

In this paper we propose a mathematical framework that can be used for defining cohomology of digital images. We state the Eilenberg-Steenrod axioms and the Universal Coefficient Theorem for this cohomology theory. We show that the Künneth formula doesn’t hold. A cup product is defined and its main properties are proved. 2010 Mathematics Subject Classification. 55N99, 68R99, 68U05, 68U10.

There exist several methods for calculating the fractal dimension of objects represented as 2D digital images. For example, Box counting, Minkowski dilation or Fourier analysis can be employed. However, there appear to be some limitations. It is not possible to calculate only the fractal dimension of an irregular region of interest in an image or to perform the calculations in a particular dire...