Path openings and closings

This paper lays the theoretical foundations to path openings and closings. The traditional morphological filter used for the analysis of linear structures in images is the union of openings (or the intersection of closings) by linear segments. However structures in images are rarely strictly straight, and as a result a more flexible approach is needed. An extension to the idea of using straight line segments as structuring elements is to use constrained paths, i.e. discrete, one-pixel thick successions of pixels oriented in a particular direction, but in general forming curved lines rather than perfectly straight lines. However the number of such paths is prohibitive and the resulting algorithm by simple composition is inefficient. In this paper we propose a way to compute openings and closings over large numbers of constrained, oriented paths in an efficient manner, suitable for building filters with applications to the analysis of oriented features, such as for example texture

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Flat zones filtering, connected operators, and filters by reconstruction

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version

Parsimonious Path Openings and Closings

International audiencePath openings and closings are morphological tools used to preserve long, thin and tortuous structures in gray level images. They explore all paths from a defined class, and filter them with a length criterion. However, most paths are redundant, making the process generally slow. Parsimonious path openings and closings are introduced in this paper to solve this problem. These operators only consider a subset of the paths considered by classical path openings, thus achieving a substantial speed-up, while obtaining similar results. Moreover, a recently introduced one dimensional (1-D) opening algorithm is applied along each selected path. Its complexity is linear with respect to the number of pixels, independent of the size of the opening. Furthermore, it is fast for any input data accuracy (integer or floating point) and works in stream. Parsimonious path openings are also extended to incomplete paths, i.e. paths containing gaps. Noise-corrupted paths can thus be processed with the same approach and complexity. These parsimonious operators achieve a several orders of magnitude speed-up. Examples are shown for incomplete path openings, where computing times are brought from minutes to tens of milliseconds, while obtaining similar results

Do Housing Prices Reflect Environmental Health Risks? Evidence from More than 1600 Toxic Plant Openings and Closings

A ubiquitous and largely unquestioned assumption in studies of housing markets is that there is perfect information about local amenities. This paper measures the housing market and health impacts of 1,600 openings and closings of industrial plants that emit toxic pollutants. We find that housing values within one mile decrease by 1.5 percent when plants open, and increase by 1.5 percent when plants close. This implies an aggregate loss in housing values per plant of about $1.5 million. While the housing value impacts are concentrated within 1/2 mile, we find statistically significant infant health impacts up to one mile away

Efficient geodesic attribute thinnings based on the barycentric diameter

International audienceAn attribute opening is an idempotent, anti-extensive and increasing operator, which removes from an image connected components which do not fulfil a given criterion. When the increasingness property is dropped, we obtain a - more general - attribute thinning. In this paper, we propose efficient grey scale thinnings based on geodesic attributes. Given that the geodesic diameter is time consuming, we propose a new geodesic attribute, the barycentric diameter to speed up the computation time. Then, we give the theoretical error bound between these two attributes, and we note that in practice, the barycentric diameter gives very similar results in comparison with the geodesic diameter. Finally, we present the algorithm with further optimisations, to obtain a 60× speed up. We illustrate the use of these thinnings in automated non-destructive material inspection: the detection of cracks. We discuss the advantages of these operators over other methods such as path openings or the supremum of openings with segments

Rubble detection from VHR aerial imagery data using differential morphological profiles

Rubble detection is a key element in post disaster crisis assessment and response procedures. In this paper we present an automated method for rapid detection and quantification of rubble from very high resolution (VHR) aerial imagery of urban regions. It is a two step procedure in which the input image is projected on to a hierarchical representation structure for efficient mining and decomposition. Image features matching the geometric and chromatic properties of rubble are fused into a rubble layer that can be re-adjusted interactively. The targeted objects are evaluated based on a density metric given by spatial aggregation. The method is tested on a small-scale exercise on the publically available aerial imagery of Port-au-Prince, Haiti. Performance and preliminary results are discussed.JRC.G.2-Global security and crisis managemen