Geometric Correspondence Research Articles

Biomedical image classification based on a cascade of an SVM with a reject option and subspace analysis

Automated biomedical image classification could confront the challenges of high level noise, image blur, illumination variation and complicated geometric correspondence among various categorical biomedical patterns in practice. To handle these challenges, we propose a cascade method consisting of two stages for biomedical image classification. At stage 1, we propose a confidence score based classification rule with a reject option for a preliminary decision using the support vector machine (SVM). The testing images going through stage 1 are separated into two groups based on their confidence scores. Those testing images with sufficiently high confidence scores are classified at stage 1 while the others with low confidence scores are rejected and fed to stage 2. At stage 2, the rejected images from stage 1 are first processed by a subspace analysis technique called eigenfeature regularization and extraction (ERE), and then classified by another SVM trained in the transformed subspace learned by ERE. At both stages, images are represented based on two types of local features, i.e., SIFT and SURF, respectively. They are encoded using various bag-of-words (BoW) models to handle biomedical patterns with and without geometric correspondence, respectively. Extensive experiments are implemented to evaluate the proposed method on three benchmark real-world biomedical image datasets. The proposed method significantly outperforms several competing state-of-the-art methods in terms of classification accuracy.

Fast and robust adaptation of organs-at-risk delineations from planning scans to match daily anatomy in pre-treatment scans for online-adaptive radiotherapy of abdominal tumors

PurposeTo validate a novel deformable image registration (DIR) method for online adaptation of planning organ-at-risk (OAR) delineations to match daily anatomy during hypo-fractionated RT of abdominal tumors. Materials and methodsFor 20 liver cancer patients, planning OAR delineations were adapted to daily anatomy using the DIR on corresponding repeat CTs. The DIR’s accuracy was evaluated for the entire cohort by comparing adapted and expert-drawn OAR delineations using geometric (Dice Similarity Coefficient (DSC), Modified Hausdorff Distance (MHD) and Mean Surface Error (MSE)) and dosimetric (Dmax and Dmean) measures. ResultsFor all OARs, DIR achieved average DSC, MHD and MSE of 86%, 2.1 mm, and 1.7 mm, respectively, within 20 s for each repeat CT. Compared to the baseline (translations), the average improvements ranged from 2% (in heart) to 24% (in spinal cord) in DSC, and 25% (in heart) to 44% (in right kidney) in MHD and MSE. Furthermore, differences in dose statistics (Dmax, Dmean and D2%) using delineations from an expert and the proposed DIR were found to be statistically insignificant (p > 0.01). ConclusionThe validated DIR showed potential for online-adaptive radiotherapy of abdominal tumors as it achieved considerably high geometric and dosimetric correspondences with the expert-drawn OAR delineations, albeit in a fraction of time required by experts.

Projector primary-based optimization for superimposed projection mappings

Recently, many researchers have focused on fully overlapping projections for three-dimensional (3-D) projection mapping systems but reproducing a high-quality appearance using this technology still remains a challenge. On top of existing color compensation-based methods, much effort is still required to faithfully reproduce an appearance that is free from artifacts, colorimetric inconsistencies, and inappropriate illuminance over the 3-D projection surface. According to our observation, this is due to the fact that overlapping projections are treated as an additive-linear mixture of color. However, this is not the case according to our elaborated observations. We propose a method that enables us to use high-quality appearance data that are measured from original objects and regenerate the same appearance by projecting optimized images using multiple projectors, ensuring that the projection-rendered results look visually close to the real object. We prepare our target appearances by photographing original objects. Then, using calibrated projector–camera pairs, we compensate for missing geometric correspondences to make our method robust against noise. The heart of our method is a target appearance-driven adaptive sampling of the projection surface followed by a representation of overlapping projections in terms of the projector-primary response. This gives off projector-primary weights to facilitate blending and the system is applied with constraints. These samples are used to populate a light transport-based system. Then, the system is solved minimizing the error to get the projection images in a noise-free manner by utilizing intersample overlaps. We ensure that we make the best utilization of available hardware resources to recreate projection mapped appearances that look as close to the original object as possible. Our experimental results show compelling results in terms of visual similarity and colorimetric error.

Geometric Correspondence Network for Camera Motion Estimation

In this paper, we propose a new learning scheme for generating geometric correspondences to be used for visual odometry. A convolutional neural network (CNN) combined with a recurrent neural networ ...

Matching Multi-Source Optical Satellite Imagery Exploiting a Multi-Stage Approach

Geometric distortions and intensity differences always exist in multi-source optical satellite imagery, seriously reducing the similarity between images, making it difficult to obtain adequate, accurate, stable, and well-distributed matches for image registration. With the goal of solving these problems, an effective image matching method is presented in this study for multi-source optical satellite imagery. The proposed method includes three steps: feature extraction, initial matching, and matching propagation. Firstly, a uniform robust scale invariant feature transform (UR-SIFT) detector was used to extract adequate and well-distributed feature points. Secondly, initial matching was conducted based on the Euclidean distance to obtain a few correct matches and the initial projective transformation between the image pair. Finally, two matching strategies were used to propagate matches and produce more reliable matching results. By using the geometric relationship between the image pair, geometric correspondence matching found more matches than the initial UR-SIFT feature points. Further probability relaxation matching propagated some new matches around the initial UR-SIFT feature points. Comprehensive experiments on Chinese ZY3 and GaoFen (GF) satellite images revealed that the proposed algorithm performs well in terms of the number of correct matches, correct matching rate, spatial distribution, and matching accuracy, compared to the standard UR-SIFT and triangulation-based propagation method.

Quantum K-theoretic geometric Satake: the case

The geometric Satake correspondence gives an equivalence of categories between the representations of a semisimple group$G$and the spherical perverse sheaves on the affine Grassmannian$Gr$of its Langlands dual group. Bezrukavnikov and Finkelberg developed a derived version of this equivalence which relates the derived category of$G^{\vee }$-equivariant constructible sheaves on$Gr$with the category of$G$-equivariant${\mathcal{O}}(\mathfrak{g})$-modules. In this paper, we develop a K-theoretic version of the derived geometric Satake which involves the quantum group$U_{q}\mathfrak{g}$. We define a convolution category$K\operatorname{Conv}(Gr)$whose morphism spaces are given by the$G^{\vee }\times \mathbb{C}^{\times }$-equivariant algebraic K-theory of certain fibre products. We conjecture that$K\operatorname{Conv}(Gr)$is equivalent to a full subcategory of the category of$U_{q}\mathfrak{g}$-equivariant${\mathcal{O}}_{q}(G)$-modules. We prove this conjecture when$G=\operatorname{SL}_{n}$. A key tool in our proof is the$\operatorname{SL}_{n}$spider, which is a combinatorial description of the category of$U_{q}\mathfrak{sl}_{n}$representations. By applying horizontal trace, we show that the annular$\operatorname{SL}_{n}$spider describes the category of$U_{q}\mathfrak{sl}_{n}$-equivariant${\mathcal{O}}_{q}(\operatorname{SL}_{n})$-modules. Then we use quantum loop algebras to relate the annular$\operatorname{SL}_{n}$spider to$K\operatorname{Conv}(Gr)$. This gives a combinatorial/diagrammatic description of both categories and proves our conjecture.

A Geometric Correspondence Feature Based-Mismatch Removal in Vision Based-Mapping and Navigation

Images with large-area repetitive texture, significant viewpoint, and illumination changes as well as occlusions often induce high-percentage keypoint mismatches, affecting the performance of vision-based mapping and navigation. Traditional methods for mismatch elimination tend to fail when the percentage of mismatches is high. In order to remove mismatches effectively, a new geometry-based approach is proposed in this paper, where Geometric Correspondence Feature (<small>GCF</small>) is used to represent the tentative correspondence. Based on the clustering property of <small>GCFs</small> from correct matches, a new clustering algorithm is developed to identify the cluster formed by the correct matches. With the defined quality factor calculated from the identified cluster, a Progressive Sample Consensus (<small>PROSAC</small>) process integrated with hyperplane-model is employed to further eliminate mismatches. Extensive experiments based on both simulated and real images in indoor and outdoor environments have demonstrated that the proposed approach can significantly improve the performance of mismatch elimination in the presence of high-percentage mismatches.

Object Segmentation Ensuring Consistency Across Multi-Viewpoint Images.

We present a hybrid approach that segments an object by using both color and depth information obtained from views captured from a low-cost RGBD camera and sparsely-located color cameras. Our system begins with generating dense depth information of each target image by using Structure from Motion and Joint Bilateral Upsampling. We formulate the multi-view object segmentation as the Markov Random Field energy optimization on the graph constructed from the superpixels. To ensure inter-view consistency of the segmentation results between color images that have too few color features, our local mapping method generates dense inter-view geometric correspondences by using the dense depth images. Finally, the pixel-based optimization step refines the boundaries of the results obtained from the superpixel-based binary segmentation. We evaluate the validity of our method under various capture conditions such as numbers of views, rotations, and distances between cameras. We compared our method with the state-of-the-art methods that use the standard multi-view datasets. The comparison verified that the proposed method works very efficiently especially in a sparse wide-baseline capture environment.

Реконструкция квадратичного кремонова преобразования

The geometric correspondence between the points of two planes can be considered well defined only when base data for its establishing is available, and a construction method by which its possible on the basis of these data for each point in one plane to find the corresponding points in the other one. Quadratic Cremona transformation can be specified by pointing out in the combined plane seven pairs of corresponding points. Naturally there is a need to establish a method for constructing any number of corresponding points. An outstanding Russian geometer K.A. Andreev indicated the linear construction based on the consideration of two correlations by which for each eighth point in the one plane is found the corresponding point of the other one. But in his work was not set up a problem to construct excluded (fundamental) points of quadratic Cremona transformation specified by seven pairs of points. There are many constructive ways to obtain the quadratic transformation in the plane. For example, it can be obtained by using two pairs of projective pencils of straight lines with vertices at the fundamental points (F-points). K.A. Andreev noted that this method for establishing of quadratic correspondence spread only to those cases when all F-points are the real ones. This statement is true for the 19th century’s level of geometric science, but today it’s too categorical. The theory of imaginary elements in geometry allows to develop a universal algorithm for construction of corresponding points in a quadratic transformation, given both by real and imaginary F-points. Summarizing the K.A. Andreev task, we come to the problem of finding the fundamental points (F-points) for a quadratic transformation specified by seven pairs of corresponding points. Almost one and half century the K.A. Andreev generalized task remained unsolved. The formation of this task’s constructive solution algorithm and its practical implementation has become possible by means of modern computer geometric modeling. According to proposed algorithm, the construction of F-points is reduced to the construction of second order auxiliary curves, on which intersection are marked the required F-points. The result received in this paper is used for development of the Cremona transformations’ theory, and for further application of this theory in the practice of geometric modeling.

Geometric Correspondence Controlled by Fermionic Vertex Algebras

We review our recent results and point out further directions in understanding of the vertex algebra approach in the geometric Langlands correspondence

Twistor Geometry of Null Foliations in Complex Euclidean Space

We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface $\mathcal{Q}^n$ of dimension $n \geq 3$, and its twistor space $\mathbb{PT}$, defined to be the space of all linear subspaces of maximal dimension of $\mathcal{Q}^n$. Viewing complex Euclidean space $\mathbb{CE}^n$ as a dense open subset of $\mathcal{Q}^n$, we show how local foliations tangent to certain integrable holomorphic totally null distributions of maximal rank on $\mathbb{CE}^n$ can be constructed in terms of complex submanifolds of $\mathbb{PT}$. The construction is illustrated by means of two examples, one involving conformal Killing spinors, the other, conformal Killing-Yano $2$-forms. We focus on the odd-dimensional case, and we treat the even-dimensional case only tangentially for comparison.

$q$-randomized Robinson–Schensted–Knuth correspondences and random polymers

We introduce and study q -randomized Robinson–Schensted–Knuth (RSK) correspondences which interpolate between the classical ( q=0 ) and geometric q \nearrow1 ) RSK correspondences (the latter ones are sometimes also called tropical). For 0<q<1 our correspondences are randomized, i.e., the result of an insertion is a certain probability distribution on semistandard Young tableaux. Because of this randomness, we use the language of discrete time Markov dynamics on two-dimensional interlacing particle arrays (these arrays are in a natural bijection with semistandard tableaux). Our dynamics act nicely on a certain class of probability measures on arrays, namely, on q -Whittaker processes (which are t=0 versions of Macdonald processes of Borodin–Corwin [8]). We present four Markov dynamics which for q=0 reduce to the classical row or column RSK correspondences applied to a random input matrix with independent geometric or Bernoulli entries. Our new two-dimensional discrete time dynamics generalize and extend several known constructions. (1) The discrete time q -TASEPs studied by Borodin–Corwin [7] arise as one-dimensional marginals of our „column" dynamics. In a similar way, our“row" dynamics lead to discrete time q -PushTASEPs – new integrable particle systems in the Kardar–Parisi–Zhang universality class. We employ these new one-dimensional discrete time systems to establish a Fredholm determinantal formula for the two-sided continuous time q -PushASEP conjectured by Corwin–Petrov [23]. (2) In a certain Poisson-type limit (from discrete to continuous time), our two-dimensional dynamics reduce to the q -randomized column and row Robinson–Schensted correspondences introduced by O’Connell–Pei [59] and Borodin–Petrov [15], respectively. (3) In a scaling limit as q\nearrow1 , two of our four dynamics on interlacing arrays turn into the geometric RSK correspondences associated with log-Gamma (introduced by Seppäläinen [70] or strict-weak (introduced independently by O’Connell–Ortmann [58] and Corwin–Seppäläinen–Shen [25] directed random lattice polymers.

Efficient Variational Approach to Multimodal Registration of Anatomical and Functional Intra-Patient Tumorous Brain Data.

This paper addresses the functional localization of intra-patient images of the brain. Functional images of the brain (fMRI and PET) provide information about brain function and metabolism whereas anatomical images (MRI and CT) supply the localization of structures with high spatial resolution. The goal is to find the geometric correspondence between functional and anatomical images in order to complement and fuse the information provided by each imaging modality. The proposed approach is based on a variational formulation of the image registration problem in the frequency domain. It has been implemented as a C/C[Formula: see text] library which is invoked from a GUI. This interface is routinely used in the clinical setting by physicians for research purposes (Inscanner, Alicante, Spain), and may be used as well for diagnosis and surgical planning. The registration of anatomic and functional intra-patient images of the brain makes it possible to obtain a geometric correspondence which allows for the localization of the functional processes that occur in the brain. Through 18 clinical experiments, it has been demonstrated how the proposed approach outperforms popular state-of-the-art registration methods in terms of efficiency, information theory-based measures (such as mutual information) and actual registration error (distance in space of corresponding landmarks).

On the exotic Grassmannian and its nilpotent variety

Given a decomposition of a vector space V = V 1 ⊕ V 2 V=V_1\oplus V_2 , the direct product X \mathfrak {X} of the projective space P ( V 1 ) \mathbb {P}(V_1) with a Grassmann variety G r k ( V ) \mathrm {Gr}_k(V) can be viewed as a double flag variety for the symmetric pair ( G , K ) = ( G L ( V ) , G L ( V 1 ) × G L ( V 2 ) ) (G,K)=(\mathrm {GL}(V),\mathrm {GL}(V_1)\times \mathrm {GL}(V_2)) . Relying on the conormal variety for the action of K K on X \mathfrak {X} , we show a geometric correspondence between the K K -orbits of X \mathfrak {X} and the K K -orbits of some appropriate exotic nilpotent cone. We also give a combinatorial interpretation of this correspondence in some special cases. Our construction is inspired by a classical result of Steinberg (1976) and by the recent work of Henderson and Trapa (2012) for the symmetric pair ( G L ( V ) , S p ( V ) ) (\mathrm {GL}(V),\mathrm {Sp}(V)) .

Total positivity, Schubert positivity, and geometric Satake

Let G be a simple, simply-connected complex algebraic group, and let X⊂G∨ be the centralizer of a principal nilpotent. Ginzburg and Peterson independently related the ring of functions on X with the homology ring of the affine Grassmannian GrG. Peterson furthermore connected X to the quantum cohomology rings of partial flag varieties G/P.In this paper we study three notions of positivity for X: (1) Schubert positivity arising via Peterson's work, (2) Lusztig's total positivity and (3) Mirković–Vilonen positivity obtained from the MV-cycles in GrG. The first main theorem establishes that these three notions of positivity coincide. Our second main theorem proves a parametrization of the totally nonnegative part of X, confirming a conjecture of the second author.In type A the parametrization and relationship with Schubert positivity were proved earlier by the second author. Here we tackle the general type case and also introduce a crucial new connection with the affine Grassmannian and geometric Satake correspondence.

Animation Setup Transfer for 3D Characters

AbstractWe present a general method for transferring skeletons and skinning weights between characters with distinct mesh topologies. Our pipeline takes as inputs a source character rig (consisting of a mesh, a transformation hierarchy of joints, and skinning weights) and a target character mesh. From these inputs, we compute joint locations and orientations that embed the source skeleton in the target mesh, as well as skinning weights to bind the target geometry to the new skeleton. Our method consists of two key steps. We first compute the geometric correspondence between source and target meshes using a semi‐automatic method relying on a set of markers. The resulting geometric correspondence is then used to formulate attribute transfer as an energy minimization and filtering problem. We demonstrate our approach on a variety of source and target bipedal characters, varying in mesh topology and morphology. Several examples demonstrate that the target characters behave well when animated with either forward or inverse kinematics. Via these examples, we show that our method preserves subtle artistic variations; spatial relationships between geometry and joints, as well as skinning weight details, are accurately maintained. Our proposed pipeline opens up many exciting possibilities to quickly animate novel characters by reusing existing production assets.

La visión artificial, un nuevo aliado para el análisis de imágenes artísticas

This paper analyzes the automatic classification of scenes that are the basis of the ideation and the designing of the sculptural production of the sculptor Miquel Planas. The main purpose is to evaluate the performance of the Bag-of-Features methods, in the challenging task of categorizing scenes when scenes differ in semantics rather than the objects they contain. We have employed a kernel-based recognition method that works by computing rough geometric correspondence on a global scale using the pyramid matching scheme introduced by Lazebnik, Schmid and Ponce in 2006. Results are promising, on average the score is about 70%. Experiments suggest that the automatic categorization of images based on computer vision methods can provide objective principles in cataloging images.

Automatic cortical surface reconstruction of high-resolution T1 echo planar imaging data

Echo planar imaging (EPI) is the method of choice for the majority of functional magnetic resonance imaging (fMRI), yet EPI is prone to geometric distortions and thus misaligns with conventional anatomical reference data. The poor geometric correspondence between functional and anatomical data can lead to severe misplacements and corruption of detected activation patterns. However, recent advances in imaging technology have provided EPI data with increasing quality and resolution. Here we present a framework for deriving cortical surface reconstructions directly from high-resolution EPI-based reference images that provide anatomical models exactly geometric distortion-matched to the functional data. Anatomical EPI data with 1mm isotropic voxel size were acquired using a fast multiple inversion recovery time EPI sequence (MI-EPI) at 7T, from which quantitative T1 maps were calculated. Using these T1 maps, volumetric data mimicking the tissue contrast of standard anatomical data were synthesized using the Bloch equations, and these T1-weighted data were automatically processed using FreeSurfer. The spatial alignment between T2⁎-weighted EPI data and the synthetic T1-weighted anatomical MI-EPI-based images was improved compared to the conventional anatomical reference. In particular, the alignment near the regions vulnerable to distortion due to magnetic susceptibility differences was improved, and sampling of the adjacent tissue classes outside of the cortex was reduced when using cortical surface reconstructions derived directly from the MI-EPI reference. The MI-EPI method therefore produces high-quality anatomical data that can be automatically segmented with standard software, providing cortical surface reconstructions that are geometrically matched to the BOLD fMRI data.

Spatial-Hessian-Feature-Guided Variational Model for Pan-Sharpening

In this paper, we propose a new spatial-Hessian-feature-guided variational model for pan-sharpening, which aims at obtaining a pan-sharpened multispectral (MS) image with both high spatial and spectral resolutions from a low-resolution MS image and a high-resolution panchromatic (PAN) image. First, we assume that the low-resolution MS image corresponds to the blurred and downsampled version of the high-resolution pan-sharpened MS image. Since the pan-sharpened MS image and the PAN image are two images of the same scene, the pan-sharpened MS image shares similar geometric correspondence with the PAN image. To this end, the geometric correspondence between the PAN image and the pan-sharpened MS image is learnt as spatial position consistency by interest point detection. Second, a new vectorial Hessian Frobenius norm term based on the image spatial Hessian feature is presented to constrain the special correspondence between the PAN image and the pan-sharpened MS image, as well as the intracorrelations among different bands of the pan-sharpened MS image. Based on these assumptions, a novel variational model is proposed for pan-sharpening. Accordingly, an efficient algorithm for the proposed model is designed under the operator splitting framework. Finally, the results on both simulated data and real data demonstrate the effectiveness of the proposed method in producing pan-sharpened results with high spectral quality and high spatial quality.

A combinatorial geometric Satake equivalence

The geometric Satake correspondence provides an equivalence of categories between the Satake category of spherical perverse sheaves on the affine Grassmannian and the category of representations of the dual group. In this note, we define a combinatorial version of the Satake category using irreducible components of fibres of the convolution morphism. We then prove an equivalence of coboundary categories between this combinatorial Satake category and the category of crystals of the dual group.