One-Dimensional Openings, Granulometries and Component Trees in O(1) Per Pixel

International audienceWe introduce a new, efficient and adaptable algorithm to compute openings, granulometries and the component tree for one-dimensional (1-D) signals. The algorithm requires only one scan of the signal, runs in place in per pixel, and supports any scalar data precision (integer or floating-point data). The algorithm is applied to two-dimensional images along straight lines, in arbitrary orientations. Oriented size distributions can thus be efficiently computed, and textures characterized. Extensive benchmarks are reported. They show that the proposed algorithm allows computing 1-D openings faster than existing algorithms for data precisions higher than 8 bits, and remains competitive with respect to the algorithm proposed by Van Droogenbroeck when dealing with 8-bit images. When computing granulometries, the new algorithm runs faster than any other method of the state of the art. Moreover, it allows efficient computation of 1-D component trees

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

Texture Analysis with Arbitrarily Oriented Morphological Opening and Closing

13 pagesThis paper presents a fast, streaming algorithm for 1-D morphological opening on 2-D support. The algorithm is further extended to compute the complete size distribution during a single image run. The Structuring Element (SE) can be oriented under arbitrary angle that allows us to perform different orientation-involved image analysis, such as local angle extraction, directional granulometries, \etc The algorithm processes an image in constant time irrespective of the SE orientation and size, with a minimal latency and very low memory requirements. Regardless the SE orientation, it reads and writes data strictly sequentially in the horizontal scan order. Aforementioned properties allow an efficient implementation in embedded hardware platforms that opens a new opportunity of a parallel computation, and consequently, a significant speed-up

High-resolution ab initio three-dimensional X-ray diffraction microscopy

Coherent X-ray diffraction microscopy is a method of imaging non-periodic isolated objects at resolutions only limited, in principle, by the largest scattering angles recorded. We demonstrate X-ray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative analysis of the reconstructed volume images. These images are retrieved from the 3D diffraction data using no a priori knowledge about the shape or composition of the object, which has never before been demonstrated on a non-periodic object. We also construct 2D images of thick objects with infinite depth of focus (without loss of transverse spatial resolution). These methods can be used to image biological and materials science samples at high resolution using X-ray undulator radiation, and establishes the techniques to be used in atomic-resolution ultrafast imaging at X-ray free-electron laser sources.Comment: 22 pages, 11 figures, submitte

Spatially-Variant Directional Mathematical Morphology Operators Based on a Diffused Average Squared Gradient Field

International audienceThis paper proposes an approach for mathematical morphology operators whose structuring element can locally adapt its orientation across the pixels of the image. The orientation at each pixel is extracted by means of a diffusion process of the average squared gradient field. The resulting vector field, the average squared gradient vector flow, extends the orientation information from the edges of the objects to the homogeneous areas of the image. The provided orientation field is then used to perform a spatially variant filtering with a linear structuring element. Results of erosion, dilation, opening and closing spatially-variant on binary images prove the validity of this theoretical sound and novel approach