Yago Diez

Hanabi is NP-complete, Even for Cheaters who Look at Their Cards

This paper studies a cooperative card game called Hanabi from an algorithmic combinatorial game theory viewpoint. The aim of the game is to play cards from 1 to n in increasing order (this has to be done independently in c different colors). Cards are drawn from a deck one by one. Drawn cards are either immediately played, discarded or stored for future use (overall each player can store up to h cards). The main feature of the game is that players know the cards their partners hold (but not theirs. This information must be shared through hints). n nWe introduce a simplified mathematical model of a single-player version of the game, and show several complexity results: the game is intractable in a general setting even if we forego with the hidden information aspect of the game. On the positive side, the game can be solved in linear time for some interesting restricted cases (i.e., for small values of h and c).

Local breast density assessment using reacquired mammographic images

PURPOSEnThe aim of this paper is to evaluate the spatial glandular volumetric tissue distribution as well as the density measures provided by Volpara™ using a dataset composed of repeated pairs of mammograms, where each pair was acquired in a short time frame and in a slightly changed position of the breast.nnnMATERIALS AND METHODSnWe conducted a retrospective analysis of 99 pairs of repeatedly acquired full-field digital mammograms from 99 different patients. The commercial software Volpara™ Density Maps (Volpara Solutions, Wellington, New Zealand) is used to estimate both the global and the local glandular tissue distribution in each image. The global measures provided by Volpara™, such as breast volume, volume of glandular tissue, and volumetric breast density are compared between the two acquisitions. The evaluation of the local glandular information is performed using histogram similarity metrics, such as intersection and correlation, and local measures, such as statistics from the difference image and local gradient correlation measures.nnnRESULTSnGlobal measures showed a high correlation (breast volume R=0.99, volume of glandular tissue R=0.94, and volumetric breast density R=0.96) regardless the anode/filter material. Similarly, histogram intersection and correlation metric showed that, for each pair, the images share a high degree of information. Regarding the local distribution of glandular tissue, small changes in the angle of view do not yield significant differences in the glandular pattern, whilst changes in the breast thickness between both acquisition affect the spatial parenchymal distribution.nnnCONCLUSIONSnThis study indicates that Volpara™ Density Maps is reliable in estimating the local glandular tissue distribution and can be used for its assessment and follow-up. Volpara™ Density Maps is robust to small variations of the acquisition angle and to the beam energy, although divergences arise due to different breast compression conditions.

An efficient surface registration using smartphone

Gathering 3D object information from the multiple spatial viewpoints typically brings up the problem of surface registration. More precisely, registration is used to fuse 3D data originally acquired from different viewpoints into a common coordinate system. This step often requires the use of relatively bulky and expensive robot arms (turntables) or presents a very challenging problem if constrained to software solutions. In this paper we present a novel surface registration method, motivated by an efficient and user-friendly implementation. Our system is inspired by the idea that three out of generally six registration parameters (degrees of freedom) can be provided in advance, at least to some degree of accuracy, by today’s smartphones. Experimental evaluations demonstrated the successful point cloud registrations of

Similarity Metrics for Intensity-Based Registration Using Breast Density Maps

sim

Automated quality assessment in three-dimensional breast ultrasound images

∼10,000 points in a matter of seconds. The evaluation included comparison with state-of-the-art descriptor methods. The method’s robustness was also studied and the results using 3D data from a professional scanner showed the potential for real-world applications.

A step‐by‐step review on patient‐specific biomechanical finite element models for breast MRI to x‐ray mammography registration

In this paper, we aim to produce a realistic 2-D projection of the breast parenchymal distribution from a 3-D breast magnetic resonance image (MRI). To evaluate the accuracy of our simulation, we compare our results with the local breast density (i.e., density map) obtained from the complementary full-field digital mammogram. To achieve this goal, we have developed a fully automatic framework, which registers MRI volumes to X-ray mammograms using a subject-specific biomechanical model of the breast. The optimization step modifies the position, orientation, and elastic parameters of the breast model to perform the alignment between the images. When the model reaches an optimal solution, the MRI glandular tissue is projected and compared with the one obtained from the corresponding mammograms. To reduce the loss of information during the ray-casting, we introduce a new approach that avoids resampling the MRI volume. In the results, we focus our efforts on evaluating the agreement of the distributions of glandular tissue, the degree of structural similarity, and the correlation between the real and synthetic density maps. Our approach obtained a high-structural agreement regardless the glandularity of the breast, whilst the similarity of the glandular tissue distributions and correlation between both images increase in denser breasts. Furthermore, the synthetic images show continuity with respect to large structures in the density maps.

Hanabi is NP-hard, even for cheaters who look at their cards☆

Intensity-based registration algorithms have been widely used in medical image applications. This type of registration algorithms uses an object function to compute a transformation and optimizes a measure of similarity between the images being registered. The most common similarity metrics used in registration are sum of squared differences, mutual information and normalized cross-correlation. This paper aims to compare these similarity metrics, using common registration algorithms applied to breast density maps registration. To evaluate the results, we use the protocols for evaluation of similarity measures proposed by Skerl et al. They consist in defining a set of random directions in the parameter space of the registration algorithm and compute statistical measures, such as the accuracy, capture range, number of maxima and risk of non-convergence, along these directions. The obtained results show a better performance corresponding to normalized cross-correlation for the rigid registration algorithm, while the sum of squared difference obtains the best result for the B-Spline method.

Mapping 3D breast lesions from full-field digital mammograms using subject-specific finite element models

Consider a set P of trajectories (polygonal lines in R2), and a query given by a trajectory Q and a threshold ϵ > 0. To answer the query we wish to find all trajectories P ∈ P such that δF(P, Q) ≤ ϵ, where δF denotes the Fréchet distance. We present an approach to efficiently answer a large number of queries for the same set P. Key ingredients are (a) precomputing a spatial hash that allows us to quickly find trajectories that have endpoints near Q; (b) precomputing simplifications on all trajectories in P; (c) using the simplifications and optimizations of the decision algorithm to efficiently decide δF(P, Q) ≤ ϵ for most P ∈ P.