ISMM 2017: 13TH INTERNATIONAL SYMPOSIUM ON MATHEMATICAL MORPHOLOGY
PROGRAM FOR TUESDAY, MAY 16TH
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09:00-10:00 Session 6: Keynote Lecture 2

Invited Speaker - Dan Ciresan

09:00
TBA
SPEAKER: Dan Ciresan
10:00-11:30Coffee Break
10:30-12:10 Session 7: Oral Session - Watersheds and Hierarchies
10:30
Evaluation of combinations of watershed hierarchies
SPEAKER: unknown

ABSTRACT. The main goal of this paper is to evaluate the potential of some combinations of watershed hierarchies. We also propose a new combination based on merging level sets of hierarchies. Experiments were performed on natural image datasets and were based on evaluating the segmentations extracted from level sets of each hierarchy against the image ground truths. Our experiments show that the most of combinations studied here are superior to their individual counterparts, which opens a path for a deeper investigation on combination of hierarchies.

10:55
Prior-based Hierarchical Segmentation Highlighting Structures of Interest
SPEAKER: unknown

ABSTRACT. Image segmentation is the process of partitioning an image into a set of meaningful regions according to some criteria. Hierarchical segmentation has emerged as a major trend in this regard as it favors the emergence of important regions at different scales. On the other hand, many methods allow us to have prior information on the position of structures of interest in the images. In this paper, we present a versatile hierarchical segmentation method that takes into account any prior spatial information and outputs a hierarchical segmentation that emphasizes the contours or regions of interest while preserving the important structures in the image. Several applications are presented that illustrate the method versatility and efficiency.

11:20
Morphological Hierarchical Image Decomposition Based on Laplacian 0-Crossings
SPEAKER: unknown

ABSTRACT. A method of text detection in natural images, to be turn into an effective embedded software on a mobile device, shall be both efficient and lightweight. We observed that a simple method based on the morphological Laplace operator can do the trick: we can construct in quasi-linear time a hierarchical image decomposition / simplification based on its 0-crossings, and search for some text in the resulting tree. Yet, for this decomposition to be sound, we need 0-crossings'' to be Jordan curves, and to that aim, we rely on some discrete topology tools. Eventually, the hierarchical representation is the morphological tree of shapes of the Laplacian sign. Moreover, we provide an algorithm with linear time complexity to compute this representation. We expect that the proposed hierarchical representation can be useful in some applications other than text detection.

11:45
Watersheds on hypergraphs for data clustering
SPEAKER: unknown

ABSTRACT. We present a novel extension of watershed cuts to hypergraphs, allowing the clustering of data represented as an hypergraph, in the context of data sciences. Contrarily to the methods in the literature, instances of data are not represented as nodes, but as edges of the hypergraph. The properties associated with each instance are used to define nodes and feature vectors associated to the edges. This rich representation is unexplored and leads to a data clustering algorithm that considers the induced topology and data similarity concomitantly. We illustrate the capabilities of our method considering a dataset of movies, with promising results, demonstrating that knowledge from mathematical morphology can be successfully leveraged for data science applications. More results, the data, and the source code used in this work are available at https://github.com/015988/hypershed.

12:15-13:30Lunch Break
13:30-15:10 Session 8: Oral Session - PDE-based Morphology
13:30
PDE for Bivariate Amoeba Median Filtering
SPEAKER: Martin Welk

ABSTRACT. Amoebas are image-adaptive structuring elements for morphological filters that have been introduced by Lerallut et al. in 2005. Iterated amoeba median filtering on grey-scale images has been proven to approximate asymptotically for vanishing structuring element radius a partial differential equation (PDE) which is known in image filtering by the name of self-snakes. This approximation property helps to understand the properties of both, morphological and PDE, image filter classes. Recently, also the PDEs approximated by multivariate median filtering with non-adaptive structuring elements have been studied. Affine equivariant multivariate medians turned out to yield more favourable PDEs than the more popular L1 median. We continue this work by considering amoeba median filtering of bivariate images using affine equivariant medians. We prove a PDE approximation result for this case. We validate the result by numerical experiments on example functions sampled with high spatial resolution.

13:55
A unified approach to PDE-driven morphology for fields of orthogonal and generalized doubly-stochastic matrices
SPEAKER: unknown

ABSTRACT. In continuous morphology two nonlinear partial differential equations (PDEs) together with specialized numerical solution schemes are employed to mimic the fundamental processes of dilation and erosion on a scalar valued image. Some attempts to tackle in a likewise manner the processing of higher order data, such as color images or even matrix valued images, so-called matrix fields, have been made. However, research has been focused almost exclusively on real symmetric matrices. Fields of non-symmetric matrices, for example rotation matrices, defy a unified approach. That is the goal of this article. First, the framework for symmetric matrices is extended to complex-valued Hermitian matrices. The later offer sufficient degrees of freedom within their structures such that, in principle, any class of real matrices may be mapped in a one-to-one manner onto a suitable subset of Hermitian matrices, where image processing may take place. Second, both the linear mapping and its inverse are provided. However, the non-linearity of dilation and erosion processes requires a backprojection onto the original class of matrices. Restricted by visualization shortcomings, the steps of this procedure are applied to the set of 3D-rotation matrices and the set of generalized doubly-stochastic matrices.

14:20
Nonlocal difference operators on Graphs for interpolation on Point Clouds
SPEAKER: unknown

ABSTRACT. In this paper we introduce a new general class of partial difference operators on graphs, which interpolate between the nonlocal $\infty$-Laplacian, the Laplacian, and a family of discrete gradient operators. In this context we investigate an associated Dirichlet problem for this general class of operators and prove the existence and uniqueness of respective solutions. We propose to use this class of operators as general framework to solve many interpolation problems in a unified manner as arising, e.g., in image and point cloud processing.

14:45
Matrix-Valued Levelings for Colour Images
SPEAKER: unknown

ABSTRACT. Morphological levelings represent a useful tool for the decomposition of an image into cartoon and texture components. Moreover, they can be used to construct a morphological scale space. However, the classic construction of levelings is limited to the use of grey scale images, since an ordering of pixel values is required.

In this paper we propose an extension of morphological levelings to colour images. To this end, we consider the formulation of colour images as matrix fields and explore techniques based on the Loewner order for formulating morphological levelings in this setting. Using the matrix-valued colours we study realisations of levelings relying on both the completely discrete construction and the formulation using a partial differential equation. Experimental results confirm the potential of our matrix-based approaches for analysing texture in colour images and for extending the range of applications of levelings in a convenient way to colour image processing.

15:10-15:40Coffee Break
15:40-17:00 Session 9: Poster Session B
15:40
Topological relations between bipolar fuzzy sets based on mathematical morphology

ABSTRACT. In many domains of information processing, both vagueness, or imprecision, and bipolarity, encompassing positive and negative parts of information, are core features of the information to be modeled and processed. This led to the development of the concept of bipolar fuzzy sets, and of associated models and tools. Here we propose to extend these tools by defining set theoretical and topological relations between bipolar fuzzy sets, including intersection, inclusion, adjacency and RCC relations widely used in mereotopology, based on bipolar connectives and on mathematical morphology operators.

15:40
A Supervoxel-based Solution to Resume Segmentation for Interactive Correction by Differential Image-Foresting Transforms
SPEAKER: unknown

ABSTRACT. The foolproof segmentation of 3D anatomical structures in medical images is usually a challenging task, which makes automatic results often far from desirable and interactive repairs necessary. In the past, we introduced a first solution to resume segmentation from third-party software into an initial optimum-path forest for interactive correction by differential image foresting transforms (DIFTs). Here, we present a new method that estimates the initial forest (input segmentation) rooted at more regularly separated seed voxels to facilitate interactive editing. The forest is a supervoxel segmentation from seeds that result from a sequence of image foresting transforms to conform as much as possible the supervoxel boundaries to the boundaries of the object in the input segmentation. We demonstrate the advantages of the new method over the previous one by using a robot user, as an impartial way to correct brain segmentation in MR-T1 images.

15:40
Hierarchical segmentation based upon multi-resolution approximations and the watershed transform
SPEAKER: unknown

ABSTRACT. Image segmentation is a classical problem in image processing, which aims at defining an image partition where each identified region corresponds to some object present in the scene. The watershed algorithm is a powerful tool from mathematical morphology to perform this specific task. When applied directly to the gradient of the image to be segmented, it usually yields an over-segmented image. To address this issue, one often uses markers that roughly correspond to the locations of the objects to be segmented. The main challenge associated to marker-controlled segmentation becomes thus the determination of the markers locations. In this article, we present a novel method to select markers for the watershed algorithm based upon multi-resolution approximations. The main principle of the method is to rely on the discrete decimated wavelet transform to obtain successive approximations of the image to be segmented. The minima of the gradient image of each coarse approximation are then propagated back to the original image space and selected as markers for the watershed transform, thus defining a hierarchical structure for the detected contours. The performance of the proposed approach is evaluated by comparing its results to manually segmented images from the Berkeley segmentation database.

15:40
Out-Of-Bag Cost-Complexity pruning of random forests
SPEAKER: unknown

ABSTRACT. Random forests and randomized tree ensembles are simple and powerful predictors used for regression and classification tasks. Their capacity to generalize well and seldom over-fit across datasets is well known, though poorly understood. We apply cost-complexity pruning of individual decision trees in bagged trees, random forests, and extremely randomized trees to identify splits in the constituent decision trees that are over-fitting training data points. We introduce cost-complexity pruning of individual trees in the ensemble, which takes advantage of the Out-Of-Bag(OOB) samples available as a by-product of bootstrap aggregation in random forests. The OOB samples not used in the construction of decision tree is used to evaluate the cost complexity parameter by cross-validation, and thus the optimal subtree. These set of experiments enable us to observe the combined effect of averaging operation across trees and majority voting within their leaves, across different subtrees. We report the performance results on the datasets from the UCI repository.

15:40
Implicit Component-Graph: A Discussion
SPEAKER: unknown

ABSTRACT. Component-graphs are defined as the generalization of component-trees to images taking their values in partially ordered sets. Similarly to component-trees, component-graphs are a lossless image model, and can allow for the development of image processing approaches (e.g., antiextensive filtering, segmentation by node selection). However, component-graphs are not trees, but directed acyclic graphs. This induces a structural complexity associated to a higher combinatorial cost. These properties make the handling of component-graphs a non-trivial task. We propose a preliminary discussion on a new way of building and manipulating component-graphs, with the purpose of reaching reasonable space and time costs. Tackling these complexity issues is indeed required for actually involving component-graphs in efficient image processing approaches.

15:40
Attribute Operators for Color Images: Image Segmentation Improved by the Use of Unsupervised Segmentation Evaluation Methods
SPEAKER: unknown

ABSTRACT. Attribute openings and thinnings are morphological connected operators that remove structures from images according to a given criterion. These operators were successfully extended from binary to grayscale images, but such extension to color images is not straightforward. This paper proposes color attribute operators by a combination of color gradients and thresholding decomposition. In this approach, not only structural criteria may be applied, but also criteria based on color features and statistics. This work proposes, in a segmentation framework, two criteria based on unsupervised segmentation evaluation for improvement of color segmentation. Segmentation using our operators performed better than two state-of-the-art methods in 80% of the experiments done using 300 images.

15:40
Ultimate opening combined with area stability applied to urban scenes
SPEAKER: unknown

ABSTRACT. This paper explores the use of ultimate opening in urban analysis context. It demonstrates the efficiency of this approach for street level elevation images, derived from 3D point clouds acquired by terrestrial mobile mapping systems. An area-stability term is introduced in the residual definition, reducing the over-segmentation of the vegetation while preserving small significant regions. We compare two possible combinations of the Ultimate Opening and the Area Stability: first as a multiplicative factor, then as a subtractive term. On the one hand, multiplicative factor is very strict and many significant regions may be eliminated by the operator. On the other hand, a subtractive factor is more easily controlled according to the image dynamics. In our application, the latter provides the best results by preserving small meaningful objects such as poles and bollards while avoiding over-segmentation on more complex objects such as cars and trees.

15:40
Function Decomposition in Main and Lesser Peaks
SPEAKER: unknown

ABSTRACT. This article shows how the dynamics extinction value can be used to compute the decomposition of a function as a sum of simpler components. We show that this decomposition induces a hierarchical segmentation of the domain of definition, and a new partial ordering on nonnegative functions. Removing some of the components according to different criteria leads to new morphological operators. Their properties are discussed and illustrated in the last section. In particular, we see that thresholding on the supports’ areas simplifies textured zones, while retaining perceptually salient elements of the image.

17:30-18:30 Session 10: Special Event

50 years of the CMM - Talk by Jean Serra