On 2D constrained discrete rigid transformations

Ngo, Phuc; Kenmochi, Yukiko; Passat, Nicolas; Talbot, Hugues

doi:10.1007/s10472-014-9406-x

Cited by 8 publications

(5 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Indeed, from Eqs. (22)(23) and (40)(41), the lines of G ∆ and A(G ∆ ) have rational-coefficient equations. In particular, for two (non-colinear) such lines…”

Section: The Cellular Space H Refining the Spaces F And Gmentioning

confidence: 99%

Homotopic Affine Transformations in the 2D Cartesian Grid

et al. 2022

View full text Add to dashboard Cite

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

show abstract

“…Indeed, from Eqs. (22)(23) and (40)(41), the lines of G ∆ and A(G ∆ ) have rational-coefficient equations. In particular, for two (non-colinear) such lines…”

Section: The Cellular Space H Refining the Spaces F And Gmentioning

confidence: 99%

Homotopic Affine Transformations in the 2D Cartesian Grid

et al. 2022

View full text Add to dashboard Cite

show abstract

“…Let the set of all discrete rigid body transformations be Π. The number of such transformations of an image with n pixels on the Z 2 -lattice is M = |Π| = o(n 5 ) [56]. We assume Π is known.…”

Section: System Modelmentioning

confidence: 99%

Finite-Sample Analysis of Image Registration

Raman,

Varshney

2020

Preprint

View full text Add to dashboard Cite

We study the problem of image registration in the finite-resolution regime and characterize the error probability of algorithms as a function of properties of the transformation and the image capture noise. Specifically, we define a channel-aware Feinstein decoder to obtain upper bounds on the minimum achievable error probability under finite resolution. We specifically focus on the higher-order terms and use Berry-Esseen type CLTs to obtain a stronger characterization of the achievability condition for the problem. Then, we derive a strong type-counting result to characterize the performance of the MMI decoder in terms of the maximum likelihood decoder, in a simplified setting of the problem. We then describe how this analysis, when related to the results from the channel-aware context provide stronger characterization of the finite-sample performance of universal image registration.

show abstract

“…The number of distinct rigid transformations of images with n pixels on the Z-lattice is polynomial in n, i.e., |Π| = O(n α ) for some α ≤ 5 [29].…”

Section: B Image Transformationsmentioning

confidence: 99%

Universal joint image clustering and registration using partition information

Raman

Varshney

2017

2017 IEEE International Symposium on Information Theory (ISIT)

View full text Add to dashboard Cite

We consider the problem of universal joint clustering and registration of images and define algorithms using multivariate information functionals. We first study registering two images using maximum mutual information and prove its asymptotic optimality. We then show the shortcomings of pairwise registration in multi-image registration, and design an asymptotically optimal algorithm based on multiinformation. Further, we define a novel multivariate information functional to perform joint clustering and registration of images, and prove consistency of the algorithm. Finally, we consider registration and clustering of numerous limited-resolution images, defining algorithms that are order-optimal in scaling of number of pixels in each image with the number of images.

show abstract

On 2D constrained discrete rigid transformations

Cited by 8 publications

References 25 publications

Homotopic Affine Transformations in the 2D Cartesian Grid

Homotopic Affine Transformations in the 2D Cartesian Grid

Finite-Sample Analysis of Image Registration

Universal joint image clustering and registration using partition information

Contact Info

Product

Resources

About