The detection of thin and oriented features in an image leads to a large field of applications specifically in medical imaging, material science or remote sensing. Path openings and closings are efficient morphological operators that use flexible oriented paths as structuring elements. They are employed in a similar way to operators with rotated line segments as structuring elements, but are more effective as they can detect linear structures that are not necessarily locally perfectly straight. While their theory has always allowed paths in arbitrary dimensions, de facto implementations were only proposed in 2D. Recently, a new implementation was proposed enabling the computation of efficient d-dimensional path operators. However this implementation is limited in the sense that it is not robust to noise. Indeed, in practical applications, for path operators to be effective, structuring elements must be sufficiently long so that they correspond to the length of the desired features to be detected. Yet, path operators are increasingly sensitive to noise as their length parameter L increases. The first part of this work is dedicated to cope with this limitation. Thus, we will propose an efficient d-dimensional algorithm, the robust path operators, which use a larger family of flexible structuring elements. Given an arbitrary length parameter G, path propagation is allowed if disconnections between two pixels belonging to a path is less or equal to G and so, render it independent of L. This simple assumption leads to a constant memory bookkeeping and results in a low complexity. The developed operators have been compared qualitatively and quantitatively to other efficient methods for the detection of line-like features. As an application, robust path openings have been integrated into a complete chain of image processing for the modelling and the characterization of glass fibers reinforced polymer. Our study has also led us to focus our interest on recent morphological connected filters based on geodesic measurements. These filters are a good alternative to path operators as they are efficient at detecting the so-called "tortuous" shapes in an image which is precisely the main limitation of path operators. Combining the local robustness of the robust path operators with the ability of geodesic attribute-based filters to recover "tortuous" shapes have enabled us to propose another original algorithm, the selective and robust path operators.
