On making nD images well-composed by a self-dual local interpolation

International audienceNatural and synthetic discrete images are generally not well-composed, leading to many topological issues: connectivities in binary images are not equivalent, the Jordan Separation theorem is not true anymore, and so on. Conversely, making images well-composed solves those problems and then gives access to many powerful tools already known in mathematical morphology as the Tree of Shapes which is of our principal interest. In this paper, we present two main results: a characterization of 3D well-composed gray-valued images; and a counter-example showing that no local self-dual interpolation satisfying a classical set of properties makes well-composed images with one subdivision in 3D, as soon as we choose the mean operator to interpolate in 1D. Then, we briefly discuss various constraints that could be interesting to change to make the problem solvable in nD

3D Geometric Analysis of Tubular Objects based on Surface Normal Accumulation

This paper proposes a simple and efficient method for the reconstruction and extraction of geometric parameters from 3D tubular objects. Our method constructs an image that accumulates surface normal information, then peaks within this image are located by tracking. Finally, the positions of these are optimized to lie precisely on the tubular shape centerline. This method is very versatile, and is able to process various input data types like full or partial mesh acquired from 3D laser scans, 3D height map or discrete volumetric images. The proposed algorithm is simple to implement, contains few parameters and can be computed in linear time with respect to the number of surface faces. Since the extracted tube centerline is accurate, we are able to decompose the tube into rectilinear parts and torus-like parts. This is done with a new linear time 3D torus detection algorithm, which follows the same principle of a previous work on 2D arc circle recognition. Detailed experiments show the versatility, accuracy and robustness of our new method.Comment: in 18th International Conference on Image Analysis and Processing, Sep 2015, Genova, Italy. 201

A quasi-linear algorithm to compute the tree of shapes of n-D images

International audienceTo compute the morphological self-dual representation of images, namely the tree of shapes, the state-of-the-art algorithms do not have a satisfactory time complexity. Furthermore the proposed algorithms are only effective for 2D images and they are far from being simple to implement. That is really penalizing since a self-dual representation of images is a structure that gives rise to many powerful operators and applications, and that could be very useful for 3D images. In this paper we propose a simple-to-write algorithm to compute the tree of shapes; it works for \nD images and has a quasi-linear complexity when data quantization is low, typically 12~bits or less. To get that result, this paper introduces a novel representation of images that has some amazing properties of continuity, while remaining discrete

LBP and irregular graph pyramids

In this paper, a new codification of Local Binary Patterns (LBP) is given using graph pyramids. The LBP code characterizes the topological category (local max, min, slope, saddle) of the gray level landscape around the center region. Given a 2D grayscale image I, our goal is to obtain a simplified image which can be seen as “minimal” representation in terms of topological characterization of I. For this, a method is developed based on merging regions and Minimum Contrast Algorithm

EM Training of Hidden Markov Models for Shape Recognition Using Cyclic Strings

Shape descriptions and the corresponding matching techniques must be robust to noise and invariant to transformations for their use in recognition tasks. Most transformations are relatively easy to handle when contours are represented by strings. However, starting point invariance is difficult to achieve. One interesting possibility is the use of cyclic strings, which are strings with no starting and final points. Here we present the use of Hidden Markov Models for modelling cyclic strings and their training using Expectation Maximization. Experimental results show that our proposal outperforms other methods in the literature

Measures of Similarity Between Objects Based on Qualitative Shape Descriptions

A computational approach for comparing qualitative shape descriptions (QSDs) of objects within digital images is presented. First, the dissimilarity of qualitative features of shape is measured: (i) intuitively using conceptual neighbourhood diagrams; and (ii) mathematically using interval distances. Then, a similarity measure between QSDs is defined and tested using images of different categories of the MPEG-7-CE-Shape-1 library, images of tiles used to build mosaics, and a collection of Clipart images. The results obtained show the effectiveness of the similarity measure defined, which is invariant to translations, rotations and scaling, and which implicitly manages deformation of shape parts and incompleteness

Device-independent, real-time identification of bacterial pathogens with a metal oxide-based olfactory sensor

A novel olfactory method for bacterial species identification using an electronic nose device called the MonoNose was developed. Differential speciation of micro-organisms present in primary cultures of clinical samples could be performed by real-time identification of volatile organic compounds (VOCs) produced during microbial replication. Kinetic measurements show that the dynamic changes in headspace gas composition are orders of magnitude larger than the static differences at the end of fermentation. Eleven different, clinically relevant bacterial species were included in this study. For each of the species, two to eight different strains were used to take intra-species biodiversity into account. A total of 52 different strains were measured in an incubator at 37°C. The results show that the diagnostic specificities varied from 100% for Clostridium difficile to 67% for Enterobacter cloacae with an overall average of 87%. Pathogen identification with a MonoNose can be achieved within 6–8 h of inoculation of the culture broths. The diagnostic specificity can be improved by broth modification to improve the VOC production of the pathogens involved

Euler Well-Composedness

In this paper, we de ne a new avour of well-composedness, called Euler well-composedness, in the general setting of regular cell complexes: A regular cell complex is Euler well-composed if the Euler characteristic of the link of each boundary vertex is 1. A cell decomposi- tion of a picture I is a pair of regular cell complexes ����� K(I);K( I) such that K(I) (resp. K( I)) is a topological and geometrical model represent- ing I (resp. its complementary, I). Then, a cell decomposition of a pic- ture I is self-dual Euler well-composed if both K(I) and K( I) are Euler well-composed. We prove in this paper that, rst, self-dual Euler well- composedness is equivalent to digital well-composedness in dimension 2 and 3, and second, in dimension 4, self-dual Euler well-composedness implies digital well-composedness, though the converse is not true