matching by tone mapping photometric invariant template matching a fast pattern matching scheme termed matching by tone mapping mtm is introduced which allows matching under nonlinear tone mappings we show that when tone mapping is approximated by a piecewise constant linear function a fast computational scheme is possible requiring computational time similar to the fast implementation of normalized cross correlation ncc in fact the mtm measure can be viewed as a generalization of the ncc for nonlinear mappings and actually reduces to ncc when mappings are restricted to be linear we empirically show that the mtm is highly discriminative and robust to noise with comparable performance capability to that of the well performing mutual information but on par with ncc in terms of computation time

configurations in abelian categories ii ringel hall algebras abstract this is the second in a series on configurations in an abelian category a given a finite poset i an i configuration is a finite collection of objects j and morphisms j k or j k j k in a satisfying some axioms where j k i configurations describe how an object x in a decomposes into subobjects the first paper defined configurations and studied moduli spaces of i configurations in a using the theory of artin stacks it showed well behaved moduli stacks obj a m i a of objects and configurations in a exist when a is the abelian category coh p of coherent sheaves on a projective scheme p or mod k q of representations of a quiver q write cf obj a for the vector space of q valued constructible functions on the stack obj a motivated by the idea of ringel hall algebras we define an associative multiplication on cf obj a using pushforwards and pullbacks along 1 morphisms between configuration moduli stacks so that cf obj a is a q algebra we also study representations of cf obj a the lie subalgebra cf ind obj a of functions supported on indecomposables and other algebraic structures on cf obj a then we generalize all these ideas to stack functions sf obj a a universal generalization of constructible functions containing more information when ext i x y 0 for all x y a and i 1 or when a coh p for p a calabi yau 3 fold we construct lie algebra morphisms from stack algebras to explicit algebras which will be important in the sequels on invariants counting semistable objects in a

a review of geometric transformations for nonrigid body registration this paper provides a comprehensive and quantitative review of spatial transformations models for nonrigid image registration it explains the theoretical foundation of the models and classifies them according to this basis this results in two categories physically based models described by partial differential equations of continuum mechanics e g linear elasticity and fluid flow and basis function expansions derived from interpolation and approximation theory e g radial basis functions b splines and wavelets recent work on constraining the transformation so that it preserves the topology or is diffeomorphic is also described the final section reviews some recent evaluation studies the paper concludes by explaining under what conditions a particular transformation model is appropriate

class based feature matching across unrestricted transformations we develop a novel method for class based feature matching across large changes in viewing conditions the method is based on the property that when objects share a similar part the similarity is preserved across viewing conditions given a feature and a training set of object images we first identify the subset of objects that share this feature the transformation of the feature s appearance across viewing conditions is determined mainly by properties of the feature rather than of the object in which it is embedded therefore the transformed feature will be shared by approximately the same set of objects based on this consistency requirement corresponding features can be reliably identified from a set of candidate matches unlike previous approaches the proposed scheme compares feature appearances only in similar viewing conditions rather than across different viewing conditions as a result the scheme is not restricted to locally planar objects or affine transformations the approach also does not require examples of correct matches we show that by using the proposed method a dense set of accurate correspondences can be obtained experimental comparisons demonstrate that matching accuracy is significantly improved over previous schemes finally we show that the scheme can be successfully used for invariant object recognition

using spanning graphs for efficient image registration we provide a detailed analysis of the use of minimal spanning graphs as an alignment method for registering multimodal images this yields an efficient graph theoretic algorithm that for the first time jointly estimates both an alignment measure and a viable descent direction with respect to a parameterized class of spatial transformations we also show how prior information about the interimage modality relationship from prealigned image pairs can be incorporated into the graph based algorithm a comparison of the graph theoretic alignment measure is provided with more traditional measures based on plug in entropy estimators this highlights previously unrecognized similarities between these two registration methods our analysis gives additional insight into the tradeoffs the graph based algorithm is making and how these will manifest themselves in the registration algorithm s performance

moduli stacks and invariants of semistable objects on k3 surfaces abstract for a k3 surface x and its bounded derived category of coherent sheaves d x we have the notion of stability conditions on d x in the sense of t bridgeland in this paper we show that the moduli stack of semistable objects in d x with a fixed numerical class and a phase is represented by an artin stack of finite type over c then following d joyce s work we introduce the invariants counting semistable objects in d x and show that the invariants are independent of a choice of a stability condition

maximum likelihood image matching image matching applications such as tracking and stereo commonly use the sum of squared difference ssd measure to determine the best match however this measure is sensitive to outliers and is not robust to template variations alternative measures have also been proposed that are more robust to these issues we improve upon these using a probabilistic formulation for image matching in terms of maximum likelihood estimation that can be used for both edge template matching and gray level image matching this formulation generalizes previous edge matching methods based on distance transforms we apply the techniques to stereo matching and feature tracking uncertainty estimation techniques allow feature selection to be performed by choosing features that minimize the localization uncertainty

a penalized likelihood approach to image warping discussion a warping is a function that deforms images by mapping between image domains the choice of function is formulated statistically as maximum penalized likelihood where the likelihood measures the similarity between images after warping and the penalty is a measure of distortion of a warping the paper addresses two issues simultaneously of how to choose the warping function and how to assess the alignment a new fourier von mises image model is identified with phase differences between fourier transformed images having von mises distributions also new null set distortion criteria are proposed with each criterion uniquely minimized by a particular set of polynomial functions a conjugate gradient algorithm is used to estimate the warping function which is numerically approximated by a piecewise bilinear function the method is motivated by and used to solve three applied problems to register a remotely sensed image with a map to align microscope images obtained by using different optics and to discriminate between species of fish from photographic images

generalized assorted camera arrays robust cross channel registration and applications one popular technique for multimodal imaging is generalized assorted pixels gap where an assorted pixel array on the image sensor allows for multimodal capture unfortunately gap is limited in its applicability because of the need for multimodal filters that are amenable with semiconductor fabrication processes and results in a fixed multimodal imaging configuration in this paper we advocate for generalized assorted camera gac arrays for multimodal imaging i e a camera array with filters of different characteristics placed in front of each camera aperture the gac provides us with three distinct advantages over gap ease of implementation flexible application dependent imaging since filters are external and can be changed and depth information that can be used for enabling novel applications e g postcapture refocusing the primary challenge in gac arrays is that since the different modalities are obtained from different viewpoints there is a need for accurate and efficient cross channel registration traditional approaches such as sum of squared differences sum of absolute differences and mutual information all result in multimodal registration errors here we propose a robust cross channel matching cost function based on aligning normalized gradients which allows us to compute cross channel subpixel correspondences for scenes exhibiting nontrivial geometry we highlight the promise of gac arrays with our cross channel normalized gradient cost for several applications such as low light imaging postcapture refocusing skin perfusion imaging using color near infrared and hyperspectral imaging

uniqueness and non uniqueness for a system of heat equations with nonlinear coupling at the boundary we study the uniqueness problem for non negative solutions of a system of two heat equations ut u vt v in a bounded smooth domain with nonlinear boundary conditions u v v u we prove that for identically zero initial data u x 0 v x 0 0 0 the zero solution is unique if and only if if pq 1 moreover in the case of non negative non trivial initial data the solution is always unique

stability conditions and extremal contractions we study extremal contractions from smooth projective varieties via a moduli theoretic approach in the two dimensional case we show that any extremal contraction appears as a moduli space of bridgeland stable objects in the derived category of coherent sheaves in the three dimensional case we show that a a similar result holds with respect to conjectural bridgeland stability conditions

moduli of pt semistable objects i abstract we show boundedness for pt semistable objects of any chern classes on a smooth projective three fold x then we show that the stack of objects in the heart coh 1 x coh 2 x 1 satisfies a version of the valuative criterion for completeness in the remainder of the paper we give a series of results on how to compute cohomology with respect to this heart

robust matching cost function for stereo correspondence using matching by tone mapping and adaptive orthogonal integral image real world stereo images are inevitably affected by radiometric differences including variations in exposure vignetting lighting and noise stereo images with severe radiometric distortion can have large radiometric differences and include locally nonlinear changes in this paper we first introduce an adaptive orthogonal integral image which is an improved version of an orthogonal integral image after that based on matching by tone mapping and the adaptive orthogonal integral image we propose a robust and accurate matching cost function that can tolerate locally nonlinear intensity distortion by using the adaptive orthogonal integral image the proposed matching cost function can adaptively construct different support regions of arbitrary shapes and sizes for different pixels in the reference image so it can operate robustly within object boundaries furthermore we develop techniques to automatically estimate the values of the parameters of our proposed function we conduct experiments using the proposed matching cost function and compare it with functions employing the census transform supporting local binary pattern and adaptive normalized cross correlation as well as a mutual information based matching cost function using different stereo data sets by using the adaptive orthogonal integral image the proposed matching cost function reduces the error from 21 51 to 15 73 in the middlebury data set and from 15 9 to 10 85 in the kitti data set as compared with using the orthogonal integral image the experimental results indicate that the proposed matching cost function is superior to the state of the art matching cost functions under radiometric variation

limit stable objects on calabi yau 3 folds the notion of limit stability is introduced in 31 to give a limiting degeneration of bridgeland stability in this article we give the survey of the results in 31 30 we introduce the limit stability counting invariants of limit stable objects and see that the wall crossing phenomena yields the rationality conjecture of pandharipandethomas generating functions

efficient registration of nonrigid 3 d bodies we present a novel method to perform an accurate registration of 3 d nonrigid bodies by using phase shift properties of the dual tree complex wavelet transform dt bbcwt since the phases of dt bbcwt coefficients change approximately linearly with the amount of feature displacement in the spatial domain motion can be estimated using the phase information from these coefficients the motion estimation is performed iteratively first by using coarser level complex coefficients to determine large motion components and then by employing finer level coefficients to refine the motion field we use a parametric affine model to describe the motion where the affine parameters are found locally by substituting into an optical flow model and by solving the resulting overdetermined set of equations from the estimated affine parameters the motion field between the sensed and the reference data sets can be generated and the sensed data set then can be shifted and interpolated spatially to align with the reference datafeature displacement set

semistable sheaves in positive characteristic we prove maruyama s conjecture on the boundedness of slope semistable sheaves on a projective variety defined over a noetherian ring our approach also gives a new proof of the boundedness for varieties defined over a characteristic zero field this result implies that in mixed characteristic the moduli spaces of gieseker semistable sheaves are projective schemes of finite type the proof uses a new inequality bounding slopes of the restriction of a sheaf to a hypersurface in terms of its slope and the discriminant this inequality also leads to effective restriction theorems in all characteristics improving earlier results in characteristic zero

a discriminative approach for wavelet denoising this paper suggests a discriminative approach for wavelet denoising where a set of mapping functions mfs are applied to the transform coefficients in an attempt to produce a noise free image as opposed to the descriptive approaches modeling image or noise priors is not required here and the mfs are learned directly from an ensemble of example images using least squares fitting the suggested scheme generates a novel set of mfs that are essentially different from the traditional soft hard thresholding in the over complete case these mfs are demonstrated to obtain comparable performance to the state of the art denoising approaches additionally this framework enables a seamless customization of the shrinkage operation to a new set of restoration problems that were not addressed previously with shrinkage techniques such as deblurring jpeg artifact removal and various types of additive noise that are not necessarily gaussian white noise

curve counting via stable pairs in the derived category for a nonsingular projective 3 fold x we define integer invariants virtually enumerating pairs c d where c x is an embedded curve and d c is a divisor a virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of x the resulting invariants are conjecturally equivalent after universal transformations to both the gromov witten and dt theories of x for calabi yau 3 folds the latter equivalence should be viewed as a wall crossing formula in the derived category

a frequency domain technique for range data registration this work introduces an original method for registering pairs of 3d views consisting of range data sets which operates in the frequency domain the fourier transform allows the decoupling of the estimate of the rotation parameters from the estimate of the translation parameters our algorithm exploits this well known property by suggesting a three step procedure the rotation parameters are estimated by the first two steps through convenient representations and projections of the fourier transforms magnitudes and the translational displacement is recovered by the third step by means of a standard phase correlation technique after compensating one of the two views for rotation the performance of the algorithm which is well suited for unsupervised registration is clearly assessed through extensive testing with several objects and shows that good and robust estimates of 3d rigid motion are achievable our algorithm can be used as a prealignment tool for more accurate space domain registration techniques like the icp algorithm

deformation obstruction theory for complexes via atiyah and kodaira spencer classes we give a universal approach to the deformation obstruction theory of objects of the derived category of coherent sheaves over a smooth projective family we recover and generalise the obstruction class of lowen and lieblich and prove that it is a product of atiyah and kodaira spencer classes this allows us to obtain deformation invariant virtual cycles on moduli spaces of objects of the derived category on threefolds

stereo processing by semiglobal matching and mutual information this paper describes the semiglobal matching sgm stereo method it uses a pixelwise mutual information ml based matching cost for compensating radiometric differences of input images pixelwise matching is supported by a smoothness constraint that is usually expressed as a global cost function sgm performs a fast approximation by pathwise optimizations from all directions the discussion also addresses occlusion detection subpixel refinement and multibaseline matching additionally postprocessing steps for removing outliers recovering from specific problems of structured environments and the interpolation of gaps are presented finally strategies for processing almost arbitrarily large images and fusion of disparity images using orthographic projection are proposed a comparison on standard stereo images shows that sgm is among the currently top ranked algorithms and is best if subpixel accuracy is considered the complexity is linear to the number of pixels and disparity range which results in a runtime of just 1 2 seconds on typical test images an in depth evaluation of the ml based matching cost demonstrates a tolerance against a wide range of radiometric transformations finally examples of reconstructions from huge aerial frame and pushbroom images demonstrate that the presented ideas are working well on practical problems

stability conditions on k3 surfaces this article contains a description of one connected component of the space of stability conditions on the bounded derived category of coherent sheaves on a complex algebraic k3 surface

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

high dimensional statistical measure for region of interest tracking this paper deals with region of interest roi tracking in video sequences the goal is to determine in successive frames the region which best matches in terms of a similarity measure a roi defined in a reference frame some tracking methods define similarity measures which efficiently combine several visual features into a probability density function pdf representation thus building a discriminative model of the roi this approach implies dealing with pdfs with domains of definition of high dimension to overcome this obstacle a standard solution is to assume independence between the different features in order to bring out low dimension marginal laws and or to make some parametric assumptions on the pdfs at the cost of generality we discard these assumptions by proposing to compute the kullback leibler divergence between high dimensional pdfs using the k th nearest neighbor framework in consequence the divergence is expressed directly from the samples i e without explicit estimation of the underlying pdfs as an application we defined 5 7 and 13 dimensional feature vectors containing color information including pixel based gradient based and patch based and spatial layout the proposed procedure performs tracking allowing for translation and scaling of the roi experiments show its efficiency on a movie excerpt and standard test sequences selected for the specific conditions they exhibit partial occlusions variations of luminance noise and complex motion

mutual information aspects of scale space images in image registration mutual information is a well performing measure based on principles of uncertainty similarly in image analysis the gaussian scale space based on minimal assumptions of the image is used to derive intrinsic properties of an image this paper starts an investigation of a combination of both methods this combination results in a double parameterized mutual information measure using local information of the image for single modality matching best response is found for coinciding parameters then critical values are found for which the parameterized mutual information has extrema first results on multi modality matching show that different parameter values instead of coinciding values yield the best response for the parameterized mutual information

on stability conditions for the quintic threefold we study the clifford type inequality for a particular type of curves c 2 2 5 which are contained in smooth quintic threefolds this allows us to prove some stronger bogomolov gieseker type inequalities for chern characters of stable sheaves and tilt stable objects on smooth quintic threefolds employing the previous framework by bayer bertram macri stellari and toda we construct an open subset of stability conditions on every smooth quintic threefold in mathbf p 4 mathbb c

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

intensity and gradient based stereo matching using hierarchical gaussian basis functions we propose a stereo correspondence method by minimizing intensity and gradient errors simultaneously in contrast to conventional use of image gradients the gradients are applied in the deformed image space although a uniform smoothness constraint is imposed it is applied only to nonfeature regions to avoid local minima in the function minimization we propose to parameterize the disparity function by hierarchical gaussians both the uniqueness and the ordering constraints can be easily imposed in our minimization framework besides we propose a method to estimate the disparity map and the camera response difference parameters simultaneously experiments with various real stereo images show robust performances of our algorithm

riemann hilbert problems from donaldson thomas theory we study a class of riemann hilbert problems arising naturally in donaldson thomas theory in certain special cases we show that these problems have unique solutions which can be written explicitly as products of gamma functions we briefly explain connections with gromov witten theory and exact wkb analysis

a pixel dissimilarity measure that is insensitive to image sampling because of image sampling traditional measures of pixel dissimilarity can assign a large value to two corresponding pixels in a stereo pair even in the absence of noise and other degrading effects we propose a measure of dissimilarity that is provably insensitive to sampling because it uses the linearly interpolated intensity functions surrounding the pixels experiments on real images show that our measure alleviates the problem of sampling with little additional computational overhead

a model based on local graphs for colour images and its application for gaussian noise smoothing in this paper a new model for processing colour images is presented a graph is built for each image pixel taking into account some constraints on links each pixel is characterized depending on the features of its related graph which allows to process it appropriately as an example we provide a characterization of each pixel based on the link cardinality of its connected component this feature enables us to properly distinguish flat image regions respect to edge and detail regions according to this we have designed a hybrid filter for colour image smoothing it combines a filter able to properly process flat image regions with another one that is more appropriate for details and texture experimental results show that our model performs appropriately we also see that our proposed filter is competitive with respect to state of the art methods it is close closer to the corresponding optimal switching filter respect to other analogous hybrid method

configurations in abelian categories iii stability conditions and identities this is the third in a series on configurations in an abelian category given a finite poset i an i configuration s p is a finite collection of objects s j and morphisms j k or in satisfying some axioms where j k are subsets of i configurations describe how an object x in decomposes into subobjects the first paper defined configurations and studied moduli spaces of configurations in using the theory of artin stacks it showed well behaved moduli stacks of objects and configurations in exist when is the abelian category coh p of coherent sheaves on a projective scheme p or of representations of a quiver q the second studied algebras of constructible functions and stack functions on this paper introduces weak stability conditions t t on we show the moduli spaces of t semistable indecomposable t semistable and t stable objects in class a are constructible sets in and some associated configuration moduli spaces constructible in so their characteristic functions and are constructible we prove many identities relating these constructible functions and their stack function analogues under pushforwards we introduce interesting algebras of constructible and stack functions and study their structure in the fourth paper we show are independent of t t and construct invariants of

the space of stability conditions on abelian threefolds and on some calabi yau threefolds we describe a connected component of the space of stability conditions on abelian threefolds and on calabi yau threefolds obtained as the crepant resolution of a finite quotient of an abelian threefold our proof includes the following essential steps 1 we simultaneously strengthen a conjecture by the first two authors and toda and prove that it follows from a more natural and seemingly weaker statement this conjecture is a bogomolov gieseker type inequality involving the third chern character of tilt stable two term complexes on smooth projective threefolds we extend it from complexes of tilt slope zero to arbitrary tilt slope 2 we show that this stronger conjecture implies the so called support property of bridgeland stability conditions and the existence of an explicit open subset of the space of stability conditions 3 we prove our conjecture for abelian threefolds thereby reproving and generalizing a result by maciocia and piyaratne important in our approach is a more systematic understanding on the behaviour of quadratic inequalities for semistable objects under wall crossing closely related to the support property

blow up problem for semilinear heat equation with absorption and a nonlocal boundary condition abstract in this paper we consider a semilinear parabolic equation u t u c x t u p for x t 0 with nonlinear and nonlocal boundary condition u 0 k x y t u l d y and nonnegative initial data where p 0 and l 0 we prove some global existence results criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data are also given

the intrinsic normal cone let x be an algebraic stack in the sense of deligne mumford we construct a purely 0 dimensional algebraic stack over x in the sense of artin the intrinsic normal cone frak c x the notion of perfect obstruction theory for x is introduced and it is shown how to construct given a perfect obstruction theory for x a pure dimensional virtual fundamental class in the chow group of x we then prove some properties of such classes both in the absolute and in the relative context via a deformation theory interpretation of obstruction theories we prove that several kinds of moduli spaces carry a natural obstruction theory and sometimes a perfect one

nonlinear registration using variational principle for mutual information we extend the multimodal image registration method described in alexander and summers fast registration algorithm using a variational principle for mutual information proc spie int soc opt eng 5032 2003 1053 1063 to nonlinear registration a variational principle maximizing mutual information leads to an euler lagrange el equation for the displacement field represented here in a basis of cubic b spline functions a cost function is constructed from the sum of squares of the residuals of the el equation at a subset of pixels where the magnitude of the spatial gradient of intensity exceeds a user chosen threshold the unknown coefficients in the displacement field representation are evaluated using a levenberg marquardt minimization procedure the proposed method was successfully applied to several image pairs of the same and different modalities and an artificially constructed series of images containing nonlinear distortions and noise

projectivity and birational geometry of bridgeland moduli spaces we construct a family of nef divisor classes on every moduli space of stable complexes in the sense of bridgeland this divisor class varies naturally with the bridgeland stability condition for a generic stability condition on a k3 surface we prove that this class is ample thereby generalizing a result of minamide yanagida and yoshioka our result also gives a systematic explanation of the relation between wall crossing for bridgeland stability and the minimal model program for the moduli space we give three applications of our method for classical moduli spaces of sheaves on a k3 surface 1 we obtain a region in the ample cone in the moduli space of gieseker stable sheaves only depending on the lattice of the k3 2 we determine the nef cone of the hilbert scheme of n points on a k3 surface of picard rank one when n is large compared to the genus 3 we verify the hassett tschinkel huybrechts sawon conjecture on the existence of a birational lagrangian fibration for the hilbert scheme in a new family of cases

donaldson thomas type invariants via microlocal geometry we prove that donaldson thomas type invariants are equal to weighted euler characteristics of their moduli spaces in particular such invariants depend only on the scheme structure of the moduli space not the symmetric obstruction theory used to define them we also introduce new invariants generalizing donaldson thomas type invariants to moduli problems with open moduli space these are useful for computing donaldson thomas type invariants over stratifications

motion estimation based on mutual information and adaptive multi scale thresholding this paper proposes a new method of calculating a matching metric for motion estimation the proposed method splits the information in the source images into multiple scale and orientation subbands reduces the subband values to a binary representation via an adaptive thresholding algorithm and uses mutual information to model the similarity of corresponding square windows in each image a moving window strategy is applied to recover a dense estimated motion field whose properties are explored the proposed matching metric is a sum of mutual information scores across space scale and orientation this facilitates the exploitation of information diversity in the source images experimental comparisons are performed amongst several related approaches revealing that the proposed matching metric is better able to exploit information diversity generating more accurate motion fields

the minimal model program for the hilbert scheme of points on p2 and bridgeland stability abstract in this paper we study the birational geometry of the hilbert scheme p 2 n of n points on p 2 we discuss the stable base locus decomposition of the effective cone and the corresponding birational models we give modular interpretations to the models in terms of moduli spaces of bridgeland semi stable objects we construct these moduli spaces as moduli spaces of quiver representations using g i t and thus show that they are projective there is a precise correspondence between wall crossings in the bridgeland stability manifold and wall crossings between mori cones for n 9 we explicitly determine the walls in both interpretations and describe the corresponding flips and divisorial contractions

mmp for moduli of sheaves on k3s via wall crossing nef and movable cones lagrangian fibrations we use wall crossing with respect to bridgeland stability conditions to systematically study the birational geometry of a moduli space m of stable sheaves on a k3 surface x a we describe the nef cone the movable cone and the effective cone of m in terms of the mukai lattice of x b we establish a long standing conjecture that predicts the existence of a birational lagrangian fibration on m whenever m admits an integral divisor class d of square zero with respect to the beauville bogomolov form these results are proved using a natural map from the space of bridgeland stability conditions mathop mathrm stab nolimits x to the cone mathop mathrm mov nolimits x of movable divisors on m this map relates wall crossing in mathop mathrm stab nolimits x to birational transformations of m in particular every minimal model of m appears as a moduli space of bridgeland stable objects on x

rigid shape matching by segmentation averaging we use segmentations to match images by shape the new matching technique does not require point to point edge correspondence and is robust to small shape variations and spatial shifts to address the unreliability of segmentations computed bottom up we give a closed form approximation to an average over all segmentations our method has many extension yielding new algorithms for tracking object detection segmentation and edge preserving smoothing for segmentation instead of a maximum a posteriori approach we compute the central segmentation minimizing the average distance to all segmentations of an image for smoothing instead of smoothing images based on local structures we smooth based on the global optimal image structures our methods for segmentation smoothing and object detection perform competitively and we also show promising results in shape based tracking

evaluation of optimization methods for nonrigid medical image registration using mutual information and b splines a popular technique for nonrigid registration of medical images is based on the maximization of their mutual information in combination with a deformation field parameterized by cubic b splines the coordinate mapping that relates the two images is found using an iterative optimization procedure this work compares the performance of eight optimization methods gradient descent with two different step size selection algorithms quasi newton nonlinear conjugate gradient kiefer wolfowitz simultaneous perturbation robbins monro and evolution strategy special attention is paid to computation time reduction by using fewer voxels to calculate the cost function and its derivatives the optimization methods are tested on manually deformed ct images of the heart on follow up ct chest scans and on mr scans of the prostate acquired using a bffe tl and t2 protocol registration accuracy is assessed by computing the overlap of segmented edges precision and convergence properties are studied by comparing deformation fields the results show that the robbins monro method is the best choice in most applications with this approach the computation time per iteration can be lowered approximately 500 times without affecting the rate of convergence by using a small subset of the image randomly selected in every iteration to compute the derivative of the mutual information from the other methods the quasi newton and the nonlinear conjugate gradient method achieve a slightly higher precision at the price of larger computation times