Anti-Geometric Diffusion for Adaptive Thresholding and Segmentation

© 2001 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Presented at the 2001 IEEE International Conference on Image Processing (ICIP 2001), 07-10 October 2001, Thessaloniki, Greece.DOI: 101109/ICIP.2001.958622In this paper, we present a novel adaptive thresholding technique based upon an anisotropic diffusion model, which may be referred to as the anti-geometric heat flow. In contrast to its more popular counterparts (such as the geometric heat flow) which diffuse parallel to image edges, this model diffuses perpendicular to image edges, yielding surfaces which are naturally suited for adaptive thresholding and segmentation. While it is possible to apply this diffusion for a fixed amount of time to detect features, we discuss how to detect features during the diffusion process, thus avoiding much of the arbitrariness associated with choosing a single scale (and makes the most notorious problem associated with anisotropic diffusion methods, namely “when do you stop?” a moot point). We will demonstrate the perfonnance of this technique on both synthetic and real images, showing applications to thresholding written text and segmentation of mehcal images and scenes

Moving-edge detection via heat flow analogy

In this paper, a new and automatic moving-edge detection algorithm is proposed, based on using the heat flow analogy. This algorithm starts with anisotropic heat diffusion in the spatial domain, to remove noise and sharpen region boundaries for the purpose of obtaining high quality edge data. Then, isotropic and linear heat diffusion is applied in the temporal domain to calculate the total amount of heat flow. The moving-edges are represented as the total amount of heat flow out from the reference frame. The overall process is completed by non-maxima suppression and hysteresis thresholding to obtain binary moving edges. Evaluation, on a variety of data, indicates that this approach can handle noise in the temporal domain because of the averaging inherent of isotropic heat flow. Results also show that this technique can detect moving-edges in image sequences, without background image subtraction

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

On Using Physical Analogies for Feature and Shape Extraction in Computer Vision

There is a rich literature of approaches to image feature extraction in computer vision. Many sophisticated approaches exist for low- and for high-level feature extraction but can be complex to implement with parameter choice guided by experimentation, but with performance analysis and optimization impeded by speed of computation. We have developed new feature extraction techniques on notional use of physical paradigms, with parametrization aimed to be more familiar to a scientifically trained user, aiming to make best use of computational resource. This paper is the first unified description of these new approaches, outlining the basis and results that can be achieved. We describe how gravitational force can be used for low-level analysis, while analogies of water flow and heat can be deployed to achieve high-level smooth shape detection, by determining features and shapes in a selection of images, comparing results with those by stock approaches from the literature. We also aim to show that the implementation is consistent with the original motivations for these techniques and so contend that the exploration of physical paradigms offers a promising new avenue for new approaches to feature extraction in computer vision

On Using Physical Analogies for Feature and Shape Extraction in Computer Vision

There is a rich literature of approaches to image feature extraction in computer vision. Many sophisticated approaches exist for low- and high-level feature extraction but can be complex to implement with parameter choice guided by experimentation, but impeded by speed of computation. We have developed new ways to extract features based on notional use of physical paradigms, with parameterisation that is more familiar to a scientifically-trained user, aiming to make best use of computational resource. We describe how analogies based on gravitational force can be used for low-level analysis, whilst analogies of water flow and heat can be deployed to achieve high-level smooth shape detection. These new approaches to arbitrary shape extraction are compared with standard state-of-art approaches by curve evolution. There is no comparator operator to our use of gravitational force. We also aim to show that the implementation is consistent with the original motivations for these techniques and so contend that the exploration of physical paradigms offers a promising new avenue for new approaches to feature extraction in computer vision

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

Hierarchies and shape-space for PET image segmentation

International audiencePositron Emission Tomography (PET) image segmentation is essential for detecting lesions and quantifying their metabolic activity. Due to the spatial and spectral properties of PET images, most methods rely on intensity-based strategies. Recent methods also propose to integrate anatomical priors to improve the segmentation process. In this article, we show how the hierarchical approaches proposed in mathematical morphology can efficiently handle these different strategies. Our contribution is twofold. First, we present the component-tree as a relevant data-structure for developing interactive , real-time, intensity-based segmentation of PET images. Second, we prove that thanks to the recent concept of shaping, we can efficiently involve a priori knowledge for lesion segmentation, while preserving the good properties of component-tree segmenta-tion. Preliminary experiments on synthetic and real PET images of lymphoma demonstrate the relevance of our approach

A Geometric Flow Approach for Segmentation of Images with Inhomongeneous Intensity and Missing Boundaries

Image segmentation is a complex mathematical problem, especially for images that contain intensity inhomogeneity and tightly packed objects with missing boundaries in between. For instance, Magnetic Resonance (MR) muscle images often contain both of these issues, making muscle segmentation especially difficult. In this paper we propose a novel intensity correction and a semi-automatic active contour based segmentation approach. The approach uses a geometric flow that incorporates a reproducing kernel Hilbert space (RKHS) edge detector and a geodesic distance penalty term from a set of markers and anti-markers. We test the proposed scheme on MR muscle segmentation and compare with some state of the art methods. To help deal with the intensity inhomogeneity in this particular kind of image, a new approach to estimate the bias field using a fat fraction image, called Prior Bias-Corrected Fuzzy C-means (PBCFCM), is introduced. Numerical experiments show that the proposed scheme leads to significantly better results than compared ones. The average dice values of the proposed method are 92.5%, 85.3%, 85.3% for quadriceps, hamstrings and other muscle groups while other approaches are at least 10% worse.Comment: Presented at CVIT 2023 Conference. Accepted to Journal of Image and Graphic

Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging

Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well-defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations $U:\mathbb{R}^{d} \rtimes S^{d-1} \to \mathbb{R}$ defined on the extended space of positions and orientations, which we relate to data on the roto-translation group $SE(d)$, $d=2,3$. This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in $SE(d)$. These curve fits minimize first or second order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on $SE(d)$. We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation $U$ and we show their advantage compared to the standard left-invariant frame on $SE(d)$. Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores