Extracting Geometric Structures in Images with Delaunay Point Processes

Favreau, Jean-Dominique; Lafarge, Florent; Bousseau, Adrien; Auvolat, Alex

doi:10.1109/tpami.2018.2890586

Cited by 17 publications

(10 citation statements)

References 48 publications

(68 reference statements)

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“…A correlated, spatial signal, such as the signal presented in Figure 1, is compressed into its M iso‐contour lines at

{ℓ}_{k = 1}^{M}

levels and the FC calls for those sensor observations that are in Δ margin of these levels. Modelling a spatial signal using its contours is a common approach that has been used in several applications, such as modelling geometric structures [16], medical image processing [17] etc. This approach is especially useful in wireless sensor networks (WSN), as it tangibly conserves energy by compressing the signal into its iso‐contour lines [18].…”

Section: Introductionmentioning

confidence: 99%

Efficient tracking of spatially correlated signals in wireless sensor fields: A weighted stochastic gradient approach

Alasti

2021

IET Wireless Sensor Systems

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A weighted stochastic gradient algorithm is proposed for cost‐efficient tracking of unknown, correlated spatial signals from randomly distributed sensor observations in localized wireless sensor field. The algorithm is implemented in spatial modelling and spatial tracking phases. In spatial modelling phase, the algorithm finds the model parameters, and in spatial tracking phase, it updates these parameters. The spatial signal is modelled with its M iso‐contour lines at equally spaced levels {ℓ}k=1M and the sensors with sensor observations in Δ margin of these contour levels report to the fusion centre (FC) for spatial monitoring purpose. Based on progressive learning and in successive iterations, the algorithm improves its findings of the signal strength's range, and the spatial, temporal and spectral attributes of the signal. To reduce the cost, in each iteration, only a subset of wireless sensors transmits the observations to the FC, in response to its query. In this article, the percentage of the reporting sensors to the FC is defined as the algorithm's cost. With importance sampling perspective, the sample space is reduced to those sensors whose observations are within a Δ margin of atleast one of these M contour levels. The Δ margin is pruned or enhanced using the proposed weighted stochastic gradient algorithm, dynamically in order to reduce the spatial tracking cost. The evaluation results show that after spatial modelling, spatial tracking is drastically of low cost and its performance is better than that of the conventional stochastic gradient method. The modelling error, the cost and the convergence of the proposed algorithm are investigated extensively, in this article. Spatial correlation in signal distribution and the coordinates of the wireless sensors are the only initial assumptions in spatial monitoring of the unknown signal distribution. The main purpose of this algorithm is low‐cost identification of unknown correlated spatial signals from sensor observations, over time. An example for application of the proposed algorithm is environmental monitoring using wireless sensor observations.

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“…A correlated, spatial signal, such as the signal presented in Figure 1, is compressed into its M iso‐contour lines at

{ℓ}_{k = 1}^{M}

Section: Introductionmentioning

confidence: 99%

Efficient tracking of spatially correlated signals in wireless sensor fields: A weighted stochastic gradient approach

Alasti

2021

IET Wireless Sensor Systems

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show abstract

“…Such a problem is traditionally solved through a two-step approach: the detection of edges or local primitives (lines, corners) followed by the retrieval of structures based on global constraints [31]. Recent works have shown the relevance of a coupled solution [12]. They remain tractable and efficient only for a limited number of structures.…”

Section: Approaches For Map Segmentationmentioning

confidence: 99%

Combining Deep Learning and Mathematical Morphology for Historical Map Segmentation

Chen¹,

Carlinet²,

Chazalon³

et al. 2021

Lecture Notes in Computer Science

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The digitization of historical maps enables the study of ancient, fragile, unique, and hardly accessible information sources. Main map features can be retrieved and tracked through the time for subsequent thematic analysis. The goal of this work is the vectorization step, i.e., the extraction of vector shapes of the objects of interest from raster images of maps. We are particularly interested in closed shape detection such as buildings, building blocks, gardens, rivers, etc. in order to monitor their temporal evolution. Historical map images present significant pattern recognition challenges. The extraction of closed shapes by using traditional Mathematical Morphology (MM) is highly challenging due to the overlapping of multiple map features and texts. Moreover, stateof-the-art Convolutional Neural Networks (CNN) are perfectly designed for content image filtering but provide no guarantee about closed shape detection. Also, the lack of textural and color information of historical maps makes it hard for CNN to detect shapes that are represented by only their boundaries. Our contribution is a pipeline that combines the strengths of CNN (efficient edge detection and filtering) and MM (guaranteed extraction of closed shapes) in order to achieve such a task. The evaluation of our approach on a public dataset shows its effectiveness for extracting the closed boundaries of objects in historical maps.

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“…But this model is very slow to simulate in practice and operates on simple synthetic images only. Delaunay point process [14] allows the sampling of vertices within a Delaunay triangulation while grouping the triangulation facets into polygons.…”

Section: Related Workmentioning

confidence: 99%

Approximating shapes in images with low-complexity polygons

Li¹,

Lafarge²,

Marlet³

2020

2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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We present an algorithm for extracting and vectorizing objects in images with polygons. Departing from a polygonal partition that oversegments an image into convex cells, the algorithm refines the geometry of the partition while labeling its cells by a semantic class. The result is a set of polygons, each capturing an object in the image. The quality of a configuration is measured by an energy that accounts for both the fidelity to input data and the complexity of the output polygons. To efficiently explore the configuration space, we perform splitting and merging operations in tandem on the cells of the polygonal partition. The exploration mechanism is controlled by a priority queue that sorts the operations most likely to decrease the energy. We show the potential of our algorithm on different types of scenes, from organic shapes to man-made objects through floor maps, and demonstrate its efficiency compared to existing vectorization methods.

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Extracting Geometric Structures in Images with Delaunay Point Processes

Cited by 17 publications

References 48 publications

Efficient tracking of spatially correlated signals in wireless sensor fields: A weighted stochastic gradient approach

Efficient tracking of spatially correlated signals in wireless sensor fields: A weighted stochastic gradient approach

Combining Deep Learning and Mathematical Morphology for Historical Map Segmentation

Approximating shapes in images with low-complexity polygons

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