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共 291 条记录，以下是21-30 订阅

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A Model is Worth Tens of Thousands of Examples 9th

A Model is Worth Tens of Thousands of Examples

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9th international conference on scale space and variational methods in computer vision, SSVM 2023

作者： Dagès, Thomas Cohen, Laurent D. Bruckstein, Alfred M. Department of Computer Science Technion Israel Institute of Technology Haifa Israel Ceremade University Paris Dauphine PSL Research University UMR CNRS 7534 Paris75016 France

ISBN: (纸本)9783031319747

Traditional signal processing methods relying on mathematical data generation models have been cast aside in favour of deep neural networks, which require vast amounts of data. Since the theoretical sample complexity is nearly impossible to evaluate, these amounts of examples are usually estimated with crude rules of thumb. However, these rules only suggest when the networks should work, but do not relate to the traditional methods. In particular, an interesting question is: how much data is required for neural networks to be on par or outperform, if possible, the traditional model-based methods? In this work, we empirically investigate this question in two simple examples, where the data is generated according to precisely defined mathematical models, and where well-understood optimal or state-of-the-art mathematical data-agnostic solutions are known. A first problem is deconvolving one-dimensional Gaussian signals and a second one is estimating a circle’s radius and location in random grayscale images of disks. By training various networks, either naive custom designed or well-established ones, with various amounts of training data, we find that networks require tens of thousands of examples in comparison to the traditional methods, whether the networks are trained from scratch or even with transfer-learning or finetuning. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Deep neural networks

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Geodesic Tracking of Retinal Vascular Trees with Optical and TV-Flow Enhancement in SE(2) 9th

Geodesic Tracking of Retinal Vascular Trees with Optical a...

引用

9th international conference on scale space and variational methods in computer vision, SSVM 2023

作者： van den Berg, Nicky J. Zhang, Shuhe Smets, Bart M. N. Berendschot, Tos T. J. M. Duits, Remco CASA Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven Netherlands Ophthalmology Department Maastricht University Maastricht Netherlands

ISBN: (纸本)9783031319747

Retinal images are often used to examine the vascular system in a non-invasive way. Studying the behavior of the vasculature on the retina allows for noninvasive diagnosis of several diseases as these vessels and their behavior are representative of the behavior of vessels throughout the human body. For early diagnosis and analysis of diseases, it is important to compare and analyze the complex vasculature in retinal images automatically. In previous work, PDE-based geometric tracking and PDE-based enhancements in the homogeneous space of positions and orientations have been studied and turned out to be useful when dealing with complex structures (crossing of blood vessels in particular). In this article, we propose a single new, more effective, Finsler function that integrates the strength of these two PDE-based approaches and additionally accounts for a number of optical effects (dehazing and illumination in particular). The results greatly improve both the previous left-invariant models and a recent data-driven model, when applied to real clinical and highly challenging images. Moreover, we show clear advantages of each module in our new single Finsler geometrical method. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Image enhancement

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Natural Numerical Networks on Directed Graphs in Satellite Image Classification 9th

Natural Numerical Networks on Directed Graphs in Satellite...

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9th international conference on scale space and variational methods in computer vision, SSVM 2023

作者： Mikula, Karol Kollár, Michal Ožvat, Aneta A. Šibíková, Mária Čahojová, Lucia Department of Mathematics Slovak University of Technology in Bratislava Radlinskeho 11 Bratislava810 05 Slovakia Algoritmy:SK s.r.o. Šulekova 6 Bratislava81106 Slovakia Plant Science and Biodiversity Center Slovak Academy of Sciences Institute of Botany Dubravska cesta 9 Bratislava845 23 Slovakia

ISBN: (纸本)9783031319747

Natural numerical networks on directed graphs as a new supervised deep learning PDE-based classification algorithm are proposed in this work. The Natural numerical network (NatNet) is based on a forward-backward diffusion model, where the points of the given clusters are attracted together by the forward diffusion, and in contrast, the backward diffusion repulses points of different clusters from each other. First, the network is trained on the labelled data to achieve the highest possible accuracy on the learning dataset. Then, the method is applied to the classification of Sentinel-2 satellite optical data to automatically identify the protected oak habitat in Western Slovakia due to its threatened status. To that goal, the relevancy map, one of the outputs of the Natural numerical network, is created efficiently;its construction is significantly speed up thanks to the new NatNet formulation on directed graphs. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Numerical methods

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Stochastic Gradient Descent for Linear Inverse Problems in Variable Exponent Lebesgue spaces 9th

Stochastic Gradient Descent for Linear Inverse Problems in...

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9th international conference on scale space and variational methods in computer vision, SSVM 2023

作者： Lazzaretti, Marta Kereta, Zeljko Estatico, Claudio Calatroni, Luca Dip. di Matematica Università di Genova Via Dodecaneso 35 Genoa16146 Italy Department of Computer Science University College London London United Kingdom CNRS UCA Inria Laboratoire I3S Sophia-Antipolis06903 France

ISBN: (纸本)9783031319747

We consider a stochastic gradient descent (SGD) algorithm for solving linear inverse problems (e.g., CT image reconstruction) in the Banach space framework of variable exponent Lebesgue spaces (pn)(R). Such non-standard spaces have been recently proved to be the appropriate functional framework to enforce pixel-adaptive regularisation in signal and image processing applications. Compared to its use in Hilbert settings, however, the application of SGD in the Banach setting of (pn)(R) is not straightforward, due, in particular to the lack of a closed-form expression and the non-separability property of the underlying norm. In this manuscript, we show that SGD iterations can effectively be performed using the associated modular function. Numerical validation on both simulated and real CT data show significant improvements in comparison to SGD solutions both in Hilbert and other Banach settings, in particular when non-Gaussian or mixed noise is observed in the data. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Banach spaces

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Diffusion–Shock Inpainting 9th

Diffusion–Shock Inpainting

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9th international conference on scale space and variational methods in computer vision, SSVM 2023

作者： Schaefer, Kristina Weickert, Joachim Mathematical Image Analysis Group Department of Mathematics and Computer Science E1.7 Saarland University Saarbrücken66123 Germany

ISBN: (纸本)9783031319747

We propose diffusion–shock (DS) inpainting as a hitherto unexplored integrodifferential equation for filling in missing structures in images. It combines two carefully chosen components that have proven their usefulness in different applications: homogeneous diffusion inpainting and coherence-enhancing shock filtering. DS inpainting enjoys the complementary synergy of its building blocks: It offers a high degree of anisotropy along an eigendirection of the structure tensor. This enables it to connect interrupted structures over large distances. Moreover, it benefits from the sharp edge structure generated by the shock filter, and it exploits the efficient filling-in effect of homogeneous diffusion. The second order equation that underlies DS inpainting inherits a continuous maximum–minimum principle from its constituents. In contrast to other attractive second order inpainting equations such as edge-enhancing anisotropic diffusion, we can guarantee this property also for the proposed discrete algorithm. Our experiments show a performance that is comparable to or better than many linear or nonlinear, isotropic or anisotropic processes of second or fourth order. They include homogeneous diffusion, biharmonic interpolation, TV inpainting, edge-enhancing anisotropic diffusion, the methods of Tschumperlé and of Bornemann and März, Cahn–Hilliard inpainting, and Euler’s elastica. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Diffusion

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Fractional Derivative variational Model for Additive Signal Decomposition 10th

Fractional Derivative Variational Model for Additive Signal...

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10th international conference on scale space and variational methods in computer vision, SSVM 2025

作者： Girometti, Laura Lanza, Alessandro Morigi, Serena Department of Mathematics University of Bologna Bologna Italy

ISBN: (纸本)9783031923685

We present a novel variational model for the additive decomposition of 1D noisy signals. The model relies on sparsifying fractional-order derivatives of the sought-for components to capture intricate signal structures. To efficiently solve the resulting optimization problem, an alternating direction method of multipliers-based algorithm is developed. Furthermore, a bilevel optimization framework is proposed to automatically select "optimal" values of all the free parameters in the model, including the orders of the sparsified fractional derivatives. Preliminary results validate the effectiveness of the proposed approach in accurately decomposing noisy signals, even in the presence of abrupt changes. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： variational techniques

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A variational Method for Curve Extraction 10th

A Variational Method for Curve Extraction

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10th international conference on scale space and variational methods in computer vision, SSVM 2025

作者： Arthaud, Majid Chambolle, Antonin Duval, Vincent ENPC 6 Av. Blaise Pascal Champs-sur-Marne77420 France INRIA Mokaplan Paris France CEREMADE CNRS and Université Paris-Dauphine PSL Paris France

ISBN: (纸本)9783031923685

We propose a functional for extracting curves between a list of possible endpoints, based on a discretization of a variational energy and Smirnov’s decomposition theorem for vector fields. It is then used to design a bi-level minimization approach to automatically extract curves and 1D structures from an image, which is mostly unsupervised. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Functional analysis

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Inversion of Magnetic Data Using Learned Dictionaries and scale space

Inversion of Magnetic Data Using Learned Dictionaries and ...

引用

10th international conference on scale space and variational methods in computer vision, SSVM 2025

作者： Ahamed, Shadab Ghyselincks, Simon Arias, Pablo Chang Huang Kloiber, Julian Ranjbar, Yasin Tang, Jingrong Zakariaei, Niloufar Haber, Eldad Department of Physics and Astronomy University of British Columbia VancouverBC Canada Department of Earth Ocean and Atmospheric Sciences University of British Columbia VancouverBC Canada Department of Mechanical Engineering University of British Columbia VancouverBC Canada

ISBN: (纸本)9783031923685

Magnetic data inversion is an important tool in geophysics, used to infer subsurface magnetic susceptibility distributions from surface magnetic field measurements. This inverse problem is inherently ill-posed, characterized by non-unique solutions, depth ambiguity, and sensitivity to noise. Traditional inversion approaches rely on predefined regularization techniques to stabilize solutions, limiting their adaptability to complex or diverse geological scenarios. In this study, we propose an approach that integrates variable dictionary learning and scale-space methods to address these challenges. Our method employs learned dictionaries, allowing for adaptive representation of complex subsurface features that are difficult to capture with predefined bases. Additionally, we extend classical variational inversion by incorporating multi-scale representations through a scale-space framework, enabling the progressive introduction of structural detail while mitigating overfitting. We implement both fixed and dynamic dictionary learning techniques, with the latter introducing iteration-dependent dictionaries for enhanced flexibility. Using a synthetic dataset to simulate geological scenarios, we demonstrate significant improvements in reconstruction accuracy and robustness compared to conventional variational and dictionary-based methods. Our results highlight the potential of learned dictionaries, especially when coupled with scale-space dynamics, to improve model recovery and noise handling. These findings underscore the promise of our data-driven approach for advance magnetic data inversion and its applications in geophysical exploration, environmental assessment, and mineral prospecting. The code is publicly available at: https://***/ahxmeds/***. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Magnetic prospecting

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Real-Time Scene Recovery from Image scale space and Perceptual Hue Similarity 10th

Real-Time Scene Recovery from Image Scale Space and Percep...

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10th international conference on scale space and variational methods in computer vision, SSVM 2025

作者： He, Roy Y. Wang, Han City University of Hong Kong Kowloon Tong Hong Kong

ISBN: (纸本)9783031923654

Chromatic degradation is often caused by multiple factors that are difficult to retrieve after images have been acquired, making scene recovery a highly ill-posed inverse problem. In this paper, we leverage the nature of human vision and propose an effective algorithm to achieve robust and visually appealing reconstructions. Specifically, we develop a reliable method for estimating chromatic bias by averaging colors from large, blurred regions identified through scale-space analysis. We then utilize CIELAB perceptual hue similarity to determine the degree of degradation caused by transmission and backscattering. By combining these estimators, we recover the scene by adaptively discounting the bias across the image domain. We conduct numerical experiments and comparative studies to demonstrate the effectiveness of our method. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Photointerpretation

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Efficient Neural Generation of 4K Masks for Homogeneous Diffusion Inpainting 9th

Efficient Neural Generation of 4K Masks for Homogeneous Di...

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9th international conference on scale space and variational methods in computer vision, SSVM 2023

作者： Schrader, Karl Peter, Pascal Kämper, Niklas Weickert, Joachim Mathematical Image Analysis Group Faculty of Mathematics and Computer Science Campus E1.7 Saarland University Saarbrücken66041 Germany

ISBN: (纸本)9783031319747

With well-selected data, homogeneous diffusion inpainting can reconstruct images from sparse data with high quality. While 4K colour images of size 3840×2160 can already be inpainted in real time, optimising the known data for applications like image compression remains challenging: Widely used stochastic strategies can take days for a single 4K image. Recently, a first neural approach for this so-called mask optimisation problem offered high speed and good quality for small images. It trains a mask generation network with the help of a neural inpainting surrogate. However, these mask networks can only output masks for the resolution and mask density they were trained for. We solve these problems and enable mask optimisation for high-resolution images through a neuroexplicit coarse-to-fine strategy. Additionally, we improve the training and interpretability of mask networks by including a numerical inpainting solver directly into the network. This allows to generate masks for 4K images in around 0.6 s while exceeding the quality of stochastic methods on practically relevant densities. Compared to popular existing approaches, this is an acceleration of up to four orders of magnitude. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Diffusion

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