Regularized Reconstruction of a Surface from its Measured Gradient Field

Harker, Matthew; O’Leary, Paul

doi:10.1007/s10851-014-0505-4

Cited by 62 publications

(104 citation statements)

References 40 publications

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“…A similar problem is commonly known as 'shape-from-shading', where a depth field is reconstructed from images [19,[45][46][47][48][49]. In [45,46], a brief survey of existing methods is presented, together with an extremely efficient approach based on the Silvester equations, for which a freely available implementation can be found in [50]. Despite the efficiency and versatility of their method, their use of centred FD schemes results in spurious oscillations, as a chequerboard Copyright (18)) for the descending aorta computed tomography angiography data set (unprocessed).…”

Section: Reconstructing An Image From the Modified Gradient Fieldmentioning

confidence: 99%

Processing the image gradient field using a topographic primal sketch approach

Gambaruto

2015

Numer Methods Biomed Eng

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Processing the image gradient field using a topographic primal sketch approachComputer Applications in Science & Engineering (CASE) Nexus I -Campus Nord UPC, C/ Jordi Girona 2, 08034 Barcelona, Spain AbstractThe spatial derivatives of the image intensity provide topographic information that may be used to identify and segment objects. The accurate computation of the derivatives is often hampered in medical images by the presence of noise and a limited resolution. This paper focuses on accurate computation of spatial derivatives and their subsequent use to process an image gradient field directly, from which an image with improved characteristics can be reconstructed. The improvements include noise reduction, contrast enhancement, thinning object contours and the preservation of edges.Processing the gradient field directly instead of the image is shown to have numerous benefits. The approach is developed such that the steps are modular, allowing the overall method to be improved and possibly tailored to different applications. As presented, the approach relies on a topographic representation and primal sketch of an image.Comparisons with existing image processing methods on a synthetic image and different medical images show improved results and accuracy in segmentation. Here the focus is on objects with low spatial resolution, which is often the case in medical images. The methods developed show the importance of improved accuracy in derivative calculation, and the potential in processing the image gradient field directly.

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Section: Reconstructing An Image From the Modified Gradient Fieldmentioning

confidence: 99%

Processing the image gradient field using a topographic primal sketch approach

Gambaruto

2015

Numer Methods Biomed Eng

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“…where Ψ is again some estimator function; see [6,8] for some discussion. One may realise that, at this stage of the process chain of PS with integration, the images are not explicitly considered anymore.…”

Section: Construction Of Our Methods and More Related Workmentioning

confidence: 99%

“…In practice, λ can be set to any small value, so that a solution of (9) lies as close as possible to a minimiser of (8). In all our experiments we set λ := 10 −6 and z 0 as the classic PS solution followed by least-squares integration [1].…”

Section: Tikhonov Regularisation Of the Modelmentioning

confidence: 99%

Optimisation of Classic Photometric Stereo by Non-convex Variational Minimisation

et al. 2018

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Estimating shape and appearance of a three dimensional object from a given set of images is a classic research topic that is still actively pursued. Among the various techniques available, photometric stereo is distinguished by the assumption that the underlying input images are taken from the same point of view but under different lighting conditions. The most common techniques provide the shape information in terms of surface normals. In this work, we instead propose to minimise a much more natural objective function, namely the reprojection error in terms of depth. Minimising the resulting non-trivial variational model for photometric stereo allows to recover the depth of the photographed scene directly. As a solving strategy, we follow an approach based on a recently published optimisation scheme for non-convex and non-smooth cost functions.The main contributions of our paper are of theoretical nature. A technical novelty in our framework is the usage of matrix differential calculus. We supplement our approach by a detailed convergence analysis of the resulting optimisation algorithm and discuss possibilities to ease the computational complexity. At hand of an experimental evaluation we discuss important properties of the method. Overall, our strategy achieves more accurate results than competing approaches. The experiments also highlights some practical aspects of the underlying optimisation algorithm that may be of interest in a more general context. G. Radow · L. Hoeltgen · M. Breuß Chair for Applied Mathematics

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“…7(b). These were used with a widely available gradient reconstruction method [13] which reduced the corresponding RSME errors in Fig. 7(e) by a third.…”

Section: Edge Sensing For Gradient-based Reconstructionmentioning

confidence: 99%

Directionally Controlled Time-of-Flight Ranging for Mobile Sensing Platforms

Tasneem

Wang

Xie

et al. 2018

Robotics: Science and Systems XIV

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Abstract-Scanning time-of-flight (TOF) sensors obtain depth measurements by directing modulated light beams across a scene. We demonstrate that control of the directional scanning patterns can enable novel algorithms and applications. Our analysis occurs entirely in the angular domain and consists of two ideas. First, we show how to exploit the angular support of the light beam to improve reconstruction results. Second, we describe how to control the light beam direction in a way that maximizes a well-known information theoretic measure. Using these two ideas, we demonstrate novel applications such as adaptive TOF sensing, LIDAR zoom, LIDAR edge sensing for gradient-based reconstruction and energy efficient LIDAR scanning. Our contributions can apply equally to sensors using mechanical, optoelectronic or MEMS-based approaches to modulate the light beam, and we show results here on a MEMS mirror-based LIDAR system. In short, we describe new adaptive directionally controlled TOF sensing algorithms which can impact mobile sensing platforms such as robots, wearable devices and IoT nodes. Creating TOF sensors for personal drones, VR/AR glasses, IoT nodes and other miniature platforms would require transcending the energy constraints due to limited battery capacity. Recent work has addressed some aspects of TOF energy efficiency with novel illumination encodings. For example, by synchronizing illumination patterns to match sensor exposures [1], low-power reconstruction can occur for scenes with significant ambient light. Additionally, spatio-temporal encodings have been shown to be efficient for both structured light illumination [30] and TOF illumination as well [29]. I. INTRODUCTIONIn this paper, we demonstrate new efficiencies that are possible with angular control of a TOF sensor. We demonstrate this with a single LIDAR beam reflected off a microelectromechanical (MEMS) mirror. The voltages that control the MEMS actuators allow analog (continuous) TOF sensing angles. As a modulator, MEMS mirrors have well-known advantages of high-speed and fast response to control [32].

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Regularized Reconstruction of a Surface from its Measured Gradient Field

Cited by 62 publications

References 40 publications

Processing the image gradient field using a topographic primal sketch approach

Processing the image gradient field using a topographic primal sketch approach

Optimisation of Classic Photometric Stereo by Non-convex Variational Minimisation

Directionally Controlled Time-of-Flight Ranging for Mobile Sensing Platforms

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