ISMM 2017: 13TH INTERNATIONAL SYMPOSIUM ON MATHEMATICAL MORPHOLOGY
PROGRAM FOR WEDNESDAY, MAY 17TH
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09:00-10:00 Session 11: Keynote Lecture 3

Invited Speaker - Stephane Gaubert

09:00
Tropical and non-linear Perron-Frobenius methods for optimal control and zero-sum games
10:00-11:30Coffee Break
10:30-12:10 Session 12: Oral Session - Graph-based Filtering and Segmentation
10:30
Power Tree Filter: A Theoretical Framework Linking Shortest Path Filters and Minimum Spanning Tree Filters
SPEAKER: unknown

ABSTRACT. Edge-preserving image filtering is an important pre-processing step in many filtering applications. In this article, we analyze the basis of edge-preserving filters and also provide theoretical links between the MST filter, which is a recent state-of-art edge-preserving filter, and filters based on geodesics. We define shortest path filters, which are closely related to adaptive kernel based filters, and show that MST filter is an approximation to the Gamma-limit of the shortest path filters. We also propose a different approximation for the Gamma-limit that is based on union of all MSTs and show that it yields better results than that of MST approximation by reducing the leaks across object boundaries. We demonstrate the effectiveness of the proposed filter in edge-preserving smoothing by comparing it with the tree filter.

10:55
Bandeirantes: A Graph-based Approach for Curve Tracing and Boundary Tracking
SPEAKER: unknown

ABSTRACT. This work presents a novel approach for curve tracing and user-steered boundary tracking in image segmentation, named Bandeirantes. The proposed approach was devised using Image Foresting Transform with unexplored and dynamic connectivity functions, which incorporate the internal energy of the paths, at any curvature scale, resulting in better segmentation of smooth-shaped objects and leading to a better curve tracing algorithm. We analyze its theoretical properties and discuss its relations with other popular methods, such as riverbed, live wire and G-wire. We compare the methods in a curve tracing task of an automatic grading system. The results show that the new method can significantly increase the system accuracy.

11:20
Seed Robustness of Oriented Image Foresting Transform: Core Computation and the Robustness Coefficient
SPEAKER: unknown

ABSTRACT. In graph-based methods, image segmentation can be seen as a graph partition problem between sets of seed pixels. The core of a seed is the region where it can be moved without altering its segmentation. The larger the core, the greater the robustness of the method in relation to its seed positioning. In this work, we present an algorithm to compute the cores of Oriented Image Foresting Transform (OIFT), an extension of Fuzzy Connectedness and Watersheds to directed weighted graphs, and compare its performance to other methods according to a proposed evaluation measure, the Robustness Coefficient. Our analysis indicates that OIFT has a good balance between accuracy and robustness, being able to overcome several methods in some datasets.

11:45
Watershed segmentation with a controlled precision
SPEAKER: Fernand Meyer

ABSTRACT. Focusing on catchment zones which may overlap rather than on catchment basins which do not overlap allows to devise innovative segmentation strategies

12:15-13:30Lunch Break
13:30-15:10 Session 13: Oral Session - Object Detection
13:30
Distance Between Vector-valued Fuzzy Sets based on Intersection Decomposition with Applications in Object Detection
SPEAKER: unknown

ABSTRACT. We present a novel approach to measuring distance between multi-channel images, suitably represented by vector-valued fuzzy sets. We first apply the intersection decomposition transformation, based on fuzzy set operations, to vector-valued fuzzy representations to enable preservation of joint multi-channel properties represented in each pixel of the original image. Distance between two vector-valued fuzzy sets is then expressed as a (weighted) sum of distances between scalar-valued fuzzy components of the transformation. Applications to object detection and classification on multi-channel images and heterogeneous object representations are discussed and evaluated subject to several important performance metrics. It is confirmed that the proposed approach out- performs several alternative single- and multi-channel distance measures between information-rich image/object representations.

13:55
Double-sided probing by map of Asplund's distances using Logarithmic Image Processing in the framework of Mathematical Morphology
SPEAKER: unknown

ABSTRACT. We establish the link between Mathematical Morphology and the map of Asplund's distances between a probe and a grey scale function, using the Logarithmic Image Processing scalar multiplication. We demonstrate that the map is the logarithm of the ratio between a dilation and an erosion of the function by a structuring function: the probe. The dilations and erosions are mappings from the lattice of the images into the lattice of the positive functions. Using a flat structuring element, the expression of the map of Asplund's distances can be simplified with a dilation and an erosion of the image; these mappings stays in the lattice of the images. We illustrate our approach by an example of pattern matching with a non-flat structuring function.

14:20
Brain lesion detection in 3D PET images using max-trees and a new spatial context criterion
SPEAKER: unknown

ABSTRACT. In this work, we propose a new criterion based on spatial context to select relevant nodes in a max-tree representation of an image, dedicated to the detection of 3D brain tumors for 18F-FDG PET images. This criterion prevents the detected lesions from merging with surrounding physiological radiotracer uptake. A complete detection method based on this criterion is proposed, and was evaluated on five patients with brain metastases and tuberculosis, and quantitatively assessed using the true positive rates and positive predictive values. The experimental results show that the method detects all the lesions in the PET.

14:45
Statistical Threshold Selection for Path Openings to Detect Cracks
SPEAKER: Petr Dokladal

ABSTRACT. Inspired by the a contrario approach this paper proposes a way of setting the threshold when using parsimonious path filters to detect thin curvilinear structures in images.

The a contrario approach, instead of modeling the structures to detect, models the noise, to detect structures deviating from the model. In this scope, we assume noise composed of pixels that are independent random variables. Henceforth, cracks that are curvilinear sequences of bright pixels (not necessarily connected) are detected as abnormal sequences of bright pixels.

In the second part, a fast approximation of the solution based on parsimonious path openings is shown.

15:10-16:00Closing Coffee Break