Browsing by Author "Daubechies, I"

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Open Access
Artificial intelligence for art investigation: Meeting the challenge of separating x-ray images of the Ghent Altarpiece.
(Science advances, 2019-08-30) Sabetsarvestani, Z; Sober, B; Higgitt, C; Daubechies, I; Rodrigues, MRD
X-ray images of polyptych wings, or other artworks painted on both sides of their support, contain in one image content from both paintings, making them difficult for experts to "read." To improve the utility of these x-ray images in studying these artworks, it is desirable to separate the content into two images, each pertaining to only one side. This is a difficult task for which previous approaches have been only partially successful. Deep neural network algorithms have recently achieved remarkable progress in a wide range of image analysis and other challenging tasks. We, therefore, propose a new self-supervised approach to this x-ray separation, leveraging an available convolutional neural network architecture; results obtained for details from the Adam and Eve panels of the Ghent Altarpiece spectacularly improve on previous attempts.
Open Access
Bayesian crack detection in ultra high resolution multimodal images of paintings
(2013 18th International Conference on Digital Signal Processing, DSP 2013, 2013-12-06) Cornelis, B; Yang, Y; Vogelstein, JT; Dooms, A; Daubechies, I; Dunson, D
The preservation of our cultural heritage is of paramount importance. Thanks to recent developments in digital acquisition techniques, powerful image analysis algorithms are developed which can be useful non-invasive tools to assist in the restoration and preservation of art. In this paper we propose a semi-supervised crack detection method that can be used for high-dimensional acquisitions of paintings coming from different modalities. Our dataset consists of a recently acquired collection of images of the Ghent Altarpiece (1432), one of Northern Europe's most important art masterpieces. Our goal is to build a classifier that is able to discern crack pixels from the background consisting of non-crack pixels, making optimal use of the information that is provided by each modality. To accomplish this we employ a recently developed non-parametric Bayesian classifier, that uses tensor factorizations to characterize any conditional probability. A prior is placed on the parameters of the factorization such that every possible interaction between predictors is allowed while still identifying a sparse subset among these predictors. The proposed Bayesian classifier, which we will refer to as conditional Bayesian tensor factorization or CBTF, is assessed by visually comparing classification results with the Random Forest (RF) algorithm. © 2013 IEEE.
Open Access
Expression of Fractals Through Neural Network Functions
Dym, N; Sober, B; Daubechies, I
To help understand the underlying mechanisms of neural networks (NNs), several groups have, in recent years, studied the number of linear regions $\ell$ of piecewise linear functions generated by deep neural networks (DNN). In particular, they showed that $\ell$ can grow exponentially with the number of network parameters $p$, a property often used to explain the advantages of DNNs over shallow NNs in approximating complicated functions. Nonetheless, a simple dimension argument shows that DNNs cannot generate all piecewise linear functions with $\ell$ linear regions as soon as $\ell > p$. It is thus natural to seek to characterize specific families of functions with $\ell$ linear regions that can be constructed by DNNs. Iterated Function Systems (IFS) generate sequences of piecewise linear functions $F_k$ with a number of linear regions exponential in $k$. We show that, under mild assumptions, $F_k$ can be generated by a NN using only $\mathcal{O}(k)$ parameters. IFS are used extensively to generate, at low computational cost, natural-looking landscape textures in artificial images. They have also been proposed for compression of natural images, albeit with less commercial success. The surprisingly good performance of this fractal-based compression suggests that our visual system may lock in, to some extent, on self-similarities in images. The combination of this phenomenon with the capacity, demonstrated here, of DNNs to efficiently approximate IFS may contribute to the success of DNNs, particularly striking for image processing tasks, as well as suggest new algorithms for representing self similarities in images based on the DNN mechanism.
Open Access
Quantitative Canvas Weave Analysis Using 2-D Synchrosqueezed Transforms: Application of time-frequency analysis to art investigation
(Signal Processing Magazine, IEEE, 2015-07) Yang, Haizhao; Lu, Jianfeng; Brown, WP; Daubechies, I; Ying, Lexing
Quantitative canvas weave analysis has many applications in art investigations of paintings, including dating, forensics, and canvas rollmate identification. Traditionally, canvas analysis is based on X-radiographs. Prior to serving as a painting canvas, a piece of fabric is coated with a priming agent; smoothing its surface makes this layer thicker between and thinner right on top of weave threads. These variations affect the X-ray absorption, making the weave pattern stand out in X-ray images of the finished painting. To characterize this pattern, it is customary to visually inspect small areas within the X-radiograph and count the number of horizontal and vertical weave threads; averages of these then estimate the overall canvas weave density. The tedium of this process typically limits its practice to just a few sample regions of the canvas. In addition, it does not capture more subtle information beyond weave density, such as thread angles or variations in the weave pattern. Signal processing techniques applied to art investigation are now increasingly used to develop computer-assisted canvas weave analysis tools.
Open Access
Removal of Canvas Patterns in Digital Acquisitions of Paintings
(IEEE Transactions on Image Processing) Cornelis, B; Yang, H; Goodfriend, A; Ocon, N; Lu, J; Daubechies, I
Open Access
Stable Phase Retrieval from Locally Stable and Conditionally Connected Measurements.
(CoRR, 2020) Cheng, C; Daubechies, I; Dym, N; Lu, J
This paper is concerned with stable phase retrieval for a family of phase retrieval models we name "locally stable and conditionally connected" (LSCC) measurement schemes. For every signal $f$, we associate a corresponding weighted graph $G_f$, defined by the LSCC measurement scheme, and show that the phase retrievability of the signal $f$ is determined by the connectivity of $G_f$. We then characterize the phase retrieval stability of the signal $f$ by two measures that are commonly used in graph theory to quantify graph connectivity: the Cheeger constant of $G_f$ for real valued signals, and the algebraic connectivity of $G_f$ for complex valued signals. We use our results to study the stability of two phase retrieval models that can be cast as LSCC measurement schemes, and focus on understanding for which signals the "curse of dimensionality" can be avoided. The first model we discuss is a finite-dimensional model for locally supported measurements such as the windowed Fourier transform. For signals "without large holes", we show the stability constant exhibits only a mild polynomial growth in the dimension, in stark contrast with the exponential growth which uniform stability constants tend to suffer from; more precisely, in $R^d$ the constant grows proportionally to $d^{1/2}$, while in $C^d$ it grows proportionally to $d$. We also show the growth of the constant in the complex case cannot be reduced, suggesting that complex phase retrieval is substantially more difficult than real phase retrieval. The second model we consider is an infinite-dimensional phase retrieval problem in a principal shift invariant space. We show that despite the infinite dimensionality of this model, signals with monotone exponential decay will have a finite stability constant. In contrast, the stability bound provided by our results will be infinite if the signal's decay is polynomial.