Volume 2, Issue 1

Mathematical morphology (MM) on grayscale images is commonly performed in the discrete domain on regularly sampled data. However, if the intention is to characterize or quantify continuous-domain objects, then the discrete-domain morphology is affected by discretization errors that may be alleviated by considering the underlying continuous signal. Given a band-limited image, for example, a real image projected through a lens system, which has been correctly sampled, the continuous signal may be reconstructed. Using information from the continuous signal when applying morphology to the discrete samples can then aid in approximating the continuous morphology. Additionally, there are a number of applications where MM would be useful and the data is irregularly sampled. A common way to deal with this is to resample the data onto a regular grid. Often this creates problems where data is interpolated in areas with too few samples. In this paper, an alternative way of thinking about the morphological operators is presented. This leads to a new type of discrete operators that work on irregularly sampled data. These operators are shown to be morphological operators that are consistent with the regular, morphological operators under the same conditions, and yield accurate results under certain conditions where traditional morphology performs poorly.

The morphological discretization is most commonly used for curve and surface discretization, which has been well studied and known to have some important properties, such as preservation of topological properties (e.g., connectivity) of an original curve or surface. To reduce its high computational cost, on the other hand, an approximation of the morphological discretization, called the analytical approximation, was introduced. In this paper, we study the properties of the analytical approximation focusing on discretization of 2D curves and 3D surfaces in the form of y = f (x) (x, y Є R) and z = f (x, y) (x, y, z Є R). We employ as a structuring element for the morphological discretization, the adjacency norm ball and use only its vertices for the analytical approximation.We show that the discretization of any curve/surface by the analytical approximation can be seen as the morphological discretization of a piecewise linear approximation of the curve/surface. The analytical approximation therefore inherits the properties of the morphological discretization even when it is not equal to the morphological discretization.

The segmentation or the geometric analysis of specular objects is known as a difficult problem in the computer vision domain. It is also true for the problem of line detection where the specular reflection implies numerous false positive line detection or missing lines located on the dark parts of the object. This limitation reduces its potential use for concrete industrial applications where metallic objects are frequent. In order to overcome this limitation, a new strategy to detect thick segment is proposed. It is not based on the image gradient as usually, but rather exploits the image intensity profile defined inside a parallel strip primitive. Associated to a digital straight segment recognition algorithmwhich is robust to noise, this strategy was implemented to track metallic tubular objects in gray-level images. The efficiency of the proposed method is demonstrated through extensive tests using an actual industrial application. An alternate release intended to overcome the possible impact of the digitization process on the achieved performance is also introduced. Both strategies are discussed at the end of the article.

This article is a first attempt towards a general theory for hierarchizing non-hierarchical image segmentation method depending on a region-dissimilarity parameter which controls the desired level of simpli fication: each level of the hierarchy is “as close as possible” to the result that one would obtain with the non-hierarchical method using the corresponding scale as simplification parameter. The introduction of this hierarchization problem in the form of an optimization problem, as well as the proposed tools to tackle it, is an important contribution of the present article. Indeed, with the hierarchized version of a segmentation method, the user can just select the level in the hierarchy, controlling the desired number of regions or can leverage on any of the tools introduced in hierarchical analysis. The main example investigated in this study is the criterion proposed by Felzenszwalb and Huttenlocher for which we show that the results of the hierarchized version of the segmentation method are better than those of the original one with the added property that it satisfies the strong causality and location principles from scale-sets image analysis. An interesting perspective of thiswork, considering the current trend in computer vision, is obviously, on a specific application, to use learning techniques and train a criterion to choose the correct region.