Gap Closure in (Road) Networks Using Higher-Order Active Contours

We present a new model for the extraction of networks from images in the presence of occlusions. Such occlusions cause gaps in the extracted network that need to he closed. Using higher-order active contours, which allow the incorporation of sophisticated geometric information, we introduce a new, non-local, 'gap closure' force that causes pairs of network extremities that are close together to extend towards one another and join, thus closing the gap between them. We demonstrate the benefits of the model using the problem of road network extraction, presenting results on aerial images

Phase field models and higher-order active contours

The representation and modelling of regions is an important topic in computer vision. In this paper, we represent a region via a level set of a 'phase field' function. The function is not constrained, e.g. to be a distance function; nevertheless, phase field energies equivalent to classical active contour energies can be defined. They represent an advantageous alternative to other methods: a linear representation space; ease of implementation (a PDE with no reinitialization); neutral initialization; greater topological freedom. We extend the basic phase field model with terms that reproduce 'higher-order active contour' energies, a powerful way of including prior geometric knowledge in the active contour framework via nonlocal interactions between contour points, in addition to the above advantages, the phase field greatly simplifies the analysis and implementation of the higher-order terms. We define a phase field model that favours regions composed of thin arms meeting at junctions, combine this with image terms, and apply the model to the extraction of line networks from remote sensing images

An extended phase field higher-order active contour model for networks and its application to road network extraction from VHR satellite images.

This paper addresses the segmentation from an image of entities that have the form of a 'network', i.e. the region in the image corresponding to the entity is composed of branches joining together at junctions, e.g. road or vascular networks. We present a new phase field higher-order active contour (HOAC) prior model for network regions, and apply it to the segmentation of road networks from very high resolution satellite images. This is a hard problem for two reasons. First, the images are complex, with much 'noise' in the road region due to cars, road markings, etc., while the background is very varied, containing many features that are locally similar to roads. Second, network regions are complex to model, because they may have arbitrary topology. In particular, we address a severe limitation of a previous model in which network branch width was constrained to be similar to maximum network branch radius of curvature, thereby providing a poor model of networks with straight narrow branches or highly Curved, wide branches. To solve this problem, we propose a new HOAC prior energy term, and reformulate it as a nonlocal phase field energy. We analyse the stability of the new model, and find that in addition to solving the above problem by separating the interactions between points on the same and opposite sides of a network branch, the new model permits the modelling of two widths simultaneously. The analysis also fixes some of the model parameters in terms of network width(s). After adding a likelihood energy, we use the model to extract the road network quasi-automatically from pieces of a QuickBird image, and compare the results to other models in the literature. The results demonstrate the superiority of the new model, the importance of strong prior knowledge in general, and of the new term in particular

A theoretical and numerical study of a phase field higher-order active contour model of directed networks.

We address the problem of quasi-automatic extraction of directed networks, which have characteristic geometric features, from images. To include the necessary prior knowledge about these geometric features, we use a phase field higher-order active contour model of directed networks. The model has a large number of unphysical parameters (weights of energy terms), and can favour different geometric structures for different parameter values. To overcome this problem, we perform a stability analysis of a long, straight bar in order to find parameter ranges that favour networks. The resulting constraints necessary to produce stable networks eliminate some parameters, replace others by physical parameters such as network branch width, and place lower and upper bounds on the values of the rest. We validate the theoretical analysis via numerical experiments, and then apply the model to the problem of hydrographic network extraction from multi-spectral VHR satellite images

A multi-layer 'gas of circles' Markov random field model for the extraction of overlapping near-circular objects.

We propose a multi-layer binary Markov random field (MRF) model that assigns high probability to object configurations in the image domain consisting of an unknown number of possibly touching or overlapping near-circular objects of approximately a given size. Each layer has an associated binary field that specifies a region corresponding to objects. Overlapping objects are represented by regions in different layers. Within each layer, long-range interactions favor connected components of approximately circular shape, while regions in different layers that overlap are penalized. Used as a prior coupled with a suitable data likelihood, the model can be used for object extraction from images, e.g. cells in biological images or densely-packed tree crowns in remote sensing images. We present a theoretical and experimental analysis of the model, and demonstrate its performance on various synthetic and biomedical images

Higher-order active contour energies for gap closure

One of the main difficulties in extracting line networks from images, and in particular road networks from remote sensing images, is the existence of interruptions in the data caused, for example, by occlusions. These can lead to gaps in the extracted network that do not correspond to gaps in the real network. In this paper, we describe a higher-order active contour energy that in addition to favouring network-like regions, includes a prior term penalizing networks containing ‘nearby opposing extremities’, thereby making gaps in the extracted network less likely. The new energy term causes such extremities to attract one another during gradient descent. They thus move towards one another and join, closing the gap. To minimize the energy, we develop specific techniques to handle the high-order derivatives that appear in the gradient descent equation. We present the results of automatic extraction of networks from real remote-sensing images, showing the ability of the model to overcome interruptions

Higher Order Active Contours and their Application to the Detection of Line Networks in Satellite Imagery

We present a novel method for the incorporation of shape information into active contour models, and apply it to the extraction of line networks (e.g. road, water) from satellite imagery. The method is based on a new class of contour energies. These energies are quadratic on the space of one-chains in the image, as opposed to classical energies, which are linear. They can be expressed as double integrals on the contour, and thus incorporate non-trivial interactions between different contour points. The new energies describe families of contours that share complex geometric properties, without making reference to any particular shape. Networks fall into such a family, and to model them we make a particular choice of quadratic energy whose minima are reticulated. To optimize the energies, we use a level set approach. The forces derived from the new energies are non-local however, thus necessitating an extension of standard level set methods. Promising experimental results are obtained using real images

Higher-order active contours

We introduce a new class of active contour models that hold great promise for region and shape modelling, and we apply a special case of these models to the extraction of road networks from satellite and aerial imagery. The new models are arbitrary polynomial functionals on the space of boundaries, and thus greatly generalize the linear functionals used in classical contour energies. While classical energies are expressed as single integrals over the contour, the new energies incorporate multiple integrals, and thus describe long-range interactions between different sets of contour points. As prior terms, they describe families of contours that share complex geometric properties, without making reference to any particular shape, and they require no pose estimation. As likelihood terms, they can describe multi-point interactions between the contour and the data. To optimize the energies, we use a level set approach. The forces derived from the new energies are non-local however, thus necessitating an extension of standard level set methods. Networks are a shape family of great importance in a number of applications, including remote sensing imagery. To model them, we make a particular choice of prior quadratic energy that describes reticulated structures, and augment it with a likelihood term that couples the data at pairs of contour points to their joint geometry. Promising experimental results are shown on real images

New higher-order active contour energies for network extraction

Using the framework of higher-order active contours, we present a new quadratic continuation energy for the extraction of line networks (e.g. road, hydrographic, vascular) in the presence of occlusions. Occlusions create gaps in the data that frequently translate to gaps in the extracted network. The new energy penalizes nearby opposing extremities of the network, and thus favours the closure of the gaps created by occlusions. Nearby opposing extremities are identified using a sophisticated interaction between pairs of points on the contour. This new model allows the extraction of fully connected networks, even though occlusions violate common assumptions about the homogeneity of the interior, and high contrast with the exterior, of the network. We present experimental results on real aerial images that demonstrate the effectiveness of the new model for network extraction tasks