R. Yin, D. Dunson, B. Cornelis, B. Brown, N. Ocon, and I. Daubechies :
“Digital cradle removal in X-ray images of art paintings ,”
pp. 4299–4303
in
2014 IEEE international conference on image processing (ICIP)
(Paris, 27–30 October 2014 ).
IEEE (Piscataway, NJ ),
2014 .
incollection

Abstract
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BibTeX

We introduce an algorithm that removes the deleterious effect of cradling on X-ray images of paintings on wooden panels. The algorithm consists of a three stage procedure. Firstly, the cradled regions are located automatically. The second step consists of separating the X-ray image into a textural and image component. In the last step the algorithm learns to distinguish between the texture caused by the wooden cradle and the texture belonging to the original painted wooden panel. The results obtained with our method are compared with those obtained manually by best current practice.

@incollection {key84927847,
AUTHOR = {Rujie Yin and David Dunson and Bruno
Cornelis and Bill Brown and Noelle Ocon
and Ingrid Daubechies},
TITLE = {Digital cradle removal in {X}-ray images
of art paintings},
BOOKTITLE = {2014 {IEEE} international conference
on image processing ({ICIP})},
PUBLISHER = {IEEE},
ADDRESS = {Piscataway, NJ},
YEAR = {2014},
PAGES = {4299--4303},
DOI = {10.1109/ICIP.2014.7025873},
NOTE = {(Paris, 27--30 October 2014).},
ISBN = {9781479957514},
}
R. Yin, B. Cornelis, G. Fodor, N. Ocon, D. Dunson, and I. Daubechies :
“Removing cradle artifacts in X-ray images of paintings ,”
SIAM J. Imaging Sci.
9 : 3
(2016 ),
pp. 1247–1272 .
MR
3541996
Zbl
06665850
article

Abstract
People
BibTeX

We propose an algorithm that removes the visually unpleasant effects of cradling in X-ray images of panel paintings, with the goal of improving the X-ray image readability by art experts. The algorithm consists of three stages. In the first stage the location of the cradle is detected automatically and the grayscale inconsistency, caused by the thickness of the cradle, is corrected. In a second stage we use a method called morphological component analysis to separate the X-ray image into a so-called cartoon part and a texture part, where the latter contains mostly the wood grain from both the panel and the cradling. The algorithm next learns a Bayesian factor model that distinguishes between the texture patterns that originate from the cradle and those from other components such as the panel and/or the painting on the panel surface, and finally uses this to remove the textures associated with the cradle. We apply the algorithm to a number of historically important paintings on panel. We also show how it can be used to digitally remove stretcher artifacts from X-rays of paintings on canvas. We compare our results with those obtained manually by best current practices in art conservation as well as on a ground truth dataset, consisting of X-ray images of a painting before and after removal of the physically attached cradle.

@article {key3541996m,
AUTHOR = {Yin, Rujie and Cornelis, Bruno and Fodor,
Gabor and Ocon, Noelle and Dunson, David
and Daubechies, Ingrid},
TITLE = {Removing cradle artifacts in {X}-ray
images of paintings},
JOURNAL = {SIAM J. Imaging Sci.},
FJOURNAL = {SIAM Journal on Imaging Sciences},
VOLUME = {9},
NUMBER = {3},
YEAR = {2016},
PAGES = {1247--1272},
DOI = {10.1137/15M1053554},
NOTE = {MR:3541996. Zbl:06665850.},
ISSN = {1936-4954},
}
R. Yin, E. Monson, E. Honig, I. Daubechies, and M. Maggioni :
“Object recognition in art drawings: Transfer of a neural network ,”
pp. 2299–2303
in
2016 IEEE international conference on acoustics, speech and signal processing
(Shanghai, 20–25 March 2016 ).
IEEE (Piscataway, NJ ),
2016 .
incollection

Abstract
People
BibTeX

We consider the problem of recognizing objects in collections of art works, in view of automatically labeling, searching and organizing databases of art works. To avoid manually labelling objects, we introduce a framework for transferring a convolutional neural network (CNN), trained on available large collections of labelled natural images, to the context of drawings. We retrain both the top and the bottom layer of the network, responsible for the high-level classification output and the low-level features detection respectively, by transforming natural images into drawings. We apply this procedure to the drawings in the Jan Brueghel Wiki, and show the transferred CNN learns a discriminative metric on drawings and achieves good recognition accuracy. We also discuss why standard descriptor-based methods is problematic in the context of drawings.

@incollection {key88488772,
AUTHOR = {Yin, Rujie and Monson, Eric and Honig,
Elizabeth and Daubechies, Ingrid and
Maggioni, Mauro},
TITLE = {Object recognition in art drawings:
{T}ransfer of a neural network},
BOOKTITLE = {2016 {IEEE} international conference
on acoustics, speech and signal processing},
PUBLISHER = {IEEE},
ADDRESS = {Piscataway, NJ},
YEAR = {2016},
PAGES = {2299--2303},
DOI = {10.1109/ICASSP.2016.7472087},
NOTE = {(Shanghai, 20--25 March 2016).},
ISSN = {2379-190X},
ISBN = {9781479999880},
}
G. Fodor, B. Cornelis, R. Yin, A. Dooms, and I. Daubechies :
“Cradle removal in X-ray images of panel paintings ,”
IPOL J. Image Process. Online
7
(2017 ),
pp. 23–42 .
MR
3608123
article

Abstract
People
BibTeX

We address the problem of mitigating the visually displeasing effects of cradling in X-ray images of panel paintings. The proposed algorithm consists of three stages. In the first stage the location of the cradling is detected semi-automatically and the grayscale inconsistency, caused by the thickness of the cradling, is adjusted. In a second stage we use a blind source separation method to decompose the X-ray image into a so-called cartoon part and a texture part, where the latter contains mostly the wood grain from both the panel as well as the cradling. In the third and final stage the algorithm tries to learn the distinction between the texture patterns that originate from the cradling and those from other components such as the panel and/or the painting. The goal of the proposed research is to improve the readability of X-ray images of paintings for art experts.

@article {key3608123m,
AUTHOR = {Fodor, G\'abor and Cornelis, Bruno and
Yin, Rujie and Dooms, Ann and Daubechies,
Ingrid},
TITLE = {Cradle removal in {X}-ray images of
panel paintings},
JOURNAL = {IPOL J. Image Process. Online},
FJOURNAL = {IPOL Journal. Image Processing Online},
VOLUME = {7},
YEAR = {2017},
PAGES = {23--42},
DOI = {10.5201/ipol.2017.174},
NOTE = {MR:3608123.},
ISSN = {2105-1232},
}
R. Yin, T. Gao, Y. M. Lu, and I. Daubechies :
“A tale of two bases: Local-nonlocal regularization on image patches with convolution framelets ,”
SIAM J. Imaging Sci.
10 : 2
(2017 ),
pp. 711–750 .
MR
3650425
Zbl
06725650
ArXiv
1606.01377
article

Abstract
People
BibTeX

We propose an image representation scheme combining the local and nonlocal characterization of patches in an image. Our representation scheme can be shown to be equivalent to a tight frame constructed from convolving local bases (e.g., wavelet frames, discrete cosine transforms, etc.) with nonlocal bases (e.g., spectral basis induced by nonlinear dimension reduction on patches), and we call the resulting frame elements convolution framelets . Insight gained from analyzing the1806 proposed representation leads to a novel interpretation of a recent high-performance patch-based image processing algorithm using the point integral method (PIM) and the low dimensional manifold model (LDMM) [S. Osher, Z. Shi, and W. Zhu, “Low Dimensional Manifold Model for Image Processing”, Tech. Rep., CAM report 16-04, UCLA, Los Angeles, CA, 2016]. In particular, we show that LDMM is a weighted \( \ell_2 \) -regularization on the coefficients obtained by decomposing images into linear combinations of convolution framelets; based on this understanding, we extend the original LDMM to a reweighted version that yields further improved results. In addition, we establish the energy concentration property of convolution framelet coefficients for the setting where the local basis is constructed from a given nonlocal basis via a linear reconstruction framework; a generalization of this framework to unions of local embeddings can provide a natural setting for interpreting BM3D, one of the state-of-the-art image denoising algorithms.

@article {key3650425m,
AUTHOR = {Yin, Rujie and Gao, Tingran and Lu,
Yue M. and Daubechies, Ingrid},
TITLE = {A tale of two bases: {L}ocal-nonlocal
regularization on image patches with
convolution framelets},
JOURNAL = {SIAM J. Imaging Sci.},
FJOURNAL = {SIAM Journal on Imaging Sciences},
VOLUME = {10},
NUMBER = {2},
YEAR = {2017},
PAGES = {711--750},
DOI = {10.1137/16M1091447},
NOTE = {ArXiv:1606.01377. MR:3650425. Zbl:06725650.},
ISSN = {1936-4954},
}
R. Yin and I. Daubechies :
“Directional wavelet bases constructions with dyadic quincunx subsampling ,”
J. Fourier Anal. Appl.
24 : 3
(June 2017 ),
pp. 872–907 .
MR
3802295
Zbl
1409.42029
ArXiv
1602.05469
article

Abstract
People
BibTeX

We construct directional wavelet systems that will enable building efficient signal representation schemes with good direction selectivity. In particular, we focus on wavelet bases with dyadic quincunx subsampling. In our previous work, We show that the supports of orthonormal wavelets in our framework are discontinuous in the frequency domain, yet this irregularity constraint can be avoided in frames, even with redundancy factor less than 2. In this paper, we focus on the extension of orthonormal wavelets to biorthogonal wavelets and show that the same obstruction of regularity as in orthonormal schemes exists in biorthogonal schemes. In addition, we provide a numerical algorithm for biorthogonal wavelets construction where the dual wavelets can be optimized, though at the cost of deteriorating the primal wavelets due to the intrinsic irregularity of biorthogonal schemes.

@article {key3802295m,
AUTHOR = {Yin, Rujie and Daubechies, Ingrid},
TITLE = {Directional wavelet bases constructions
with dyadic quincunx subsampling},
JOURNAL = {J. Fourier Anal. Appl.},
FJOURNAL = {Journal of Fourier Analysis and Applications},
VOLUME = {24},
NUMBER = {3},
MONTH = {June},
YEAR = {2017},
PAGES = {872--907},
DOI = {10.1007/s00041-017-9540-z},
NOTE = {ArXiv:1602.05469. MR:3802295. Zbl:1409.42029.},
ISSN = {1069-5869},
}
R. Alaifari, I. Daubechies, P. Grohs, and R. Yin :
“Stable phase retrieval in infinite dimensions ,”
Found. Comput. Math.
19 : 4
(August 2019 ),
pp. 869–900 .
MR
3989716
Zbl
07091714
ArXiv
1609.00034
article

Abstract
People
BibTeX

The problem of phase retrieval is to determine a signal \( f\in \mathcal{H} \) , with \( \mathcal{H} \) a Hilbert space, from intensity measurements \( |F(\omega)| \) , where
\[ F(\omega):=\langle f,\phi_{\omega}\rangle \]
are measurements of \( f \) with respect to a measurement system
\[ (\phi_{\omega})_{\omega\in \Omega}\subset \mathcal{H} .\]
Although phase retrieval is always stable in the finite dimensional setting whenever it is possible (i.e. injectivity implies stability for the inverse problem), the situation is drastically different if \( \mathcal{H} \) is infinite-dimensional: in that case phase retrieval is never
uniformly stable [Cahill et al. 2016; Alaifari and Grohs 2017]; moreover the stability deteriorates severely in the dimension of the problem [Cahill et al. 2016]. On the other hand, all empirically observed instabilities are of a certain type: they occur whenever the function \( |F| \) of intensity measurements is concentrated on disjoint sets \( D_j\subset \Omega \) , i.e., when
\[ F = \sum_{j=1}^k F_j \]
where each \( F_j \) is concentrated on \( D_j \) (and \( k \geq 2 \) ). Motivated by these considerations we propose a new paradigm for stable phase retrieval by considering the problem of reconstructing \( F \) up to a phase factor that is not global, but that can be different for each of the subsets \( D_j \) , i.e., recovering \( F \) up to the equivalence
\[ F \sim \sum_{j=1}^k e^{i \alpha_j} F_j. \]
We present concrete applications (for example in audio processing) where this new notion of stability is natural and meaningful and show that in this setting stable phase retrieval can actually be achieved, for instance if the measurement system is a Gabor frame or a frame of Cauchy wavelets.

@article {key3989716m,
AUTHOR = {Alaifari, Rima and Daubechies, Ingrid
and Grohs, Philipp and Yin, Rujie},
TITLE = {Stable phase retrieval in infinite dimensions},
JOURNAL = {Found. Comput. Math.},
FJOURNAL = {Foundations of Computational Mathematics},
VOLUME = {19},
NUMBER = {4},
MONTH = {August},
YEAR = {2019},
PAGES = {869--900},
DOI = {10.1007/s10208-018-9399-7},
NOTE = {ArXiv:1609.00034. MR:3989716. Zbl:07091714.},
ISSN = {1615-3375},
}