Exploring the use of two-dimensional piecewise-linear functions as an alternative model for representing and processing grayscale-images
Victor Manuel Jimenez-Fernandez, Héctor Vázquez-Leal, Uriel Antonio Filobello-Nino, Maribel Jiménez‐Fernández, Luis Javier Morales-Mendoza, Mario González-Lee · Journal of Applied Research and Technology · 2016
Traditionally, a grayscale image is represented as a rectangular array whose internal values describe a discrete level of intensity or luminancedenoted as pixel. Due to its structure and complete compatibility with matrix operators, this representation is the most widely used in imageprocessing. Although the strong robustness of this standard is not in question, it is always enriching to have an alternative description format inorder to provide not only a different image representation scheme but also an additional approach to image processing. Motivated by this fact, in thispaper the viability of using continuous piecewise linear functions of two spatial variables as an alternative model description of grayscale imagesis explored. Moreover, the possibility of applying this type of representation in image processing is also examined by using mapping variabletransformations, here denominated as functional filters. Furthermore, it is also shown that such alternative image model can also be used in morecomplex tasks like tridimensional volume estimation. To verify this proposal, illustrative examples are reported, showing not only an inherentimprovement in the visual perception of image, but also a practical image processing capability.