40,628 research outputs found
Robust point correspondence applied to two and three-dimensional image registration
Accurate and robust correspondence calculations are very important in many medical and biological applications. Often, the correspondence calculation forms part of a rigid registration algorithm, but accurate correspondences are especially important for elastic registration algorithms and for quantifying changes over time. In this paper, a new correspondence calculation algorithm, CSM (correspondence by sensitivity to movement), is described. A robust corresponding point is calculated by determining the sensitivity of a correspondence to movement of the point being matched. If the correspondence is reliable, a perturbation in the position of this point should not result in a large movement of the correspondence. A measure of reliability is also calculated. This correspondence calculation method is independent of the registration transformation and has been incorporated into both a 2D elastic registration algorithm for warping serial sections and a 3D rigid registration algorithm for registering pre and postoperative facial range scans. These applications use different methods for calculating the registration transformation and accurate rigid and elastic alignment of images has been achieved with the CSM method. It is expected that this method will be applicable to many different applications and that good results would be achieved if it were to be inserted into other methods for calculating a registration transformation from correspondence
Solving Jigsaw Puzzles By the Graph Connection Laplacian
We propose a novel mathematical framework to address the problem of
automatically solving large jigsaw puzzles. This problem assumes a large image,
which is cut into equal square pieces that are arbitrarily rotated and
shuffled, and asks to recover the original image given the transformed pieces.
The main contribution of this work is a method for recovering the rotations of
the pieces when both shuffles and rotations are unknown. A major challenge of
this procedure is estimating the graph connection Laplacian without the
knowledge of shuffles. We guarantee some robustness of the latter estimate to
measurement errors. A careful combination of our proposed method for estimating
rotations with any existing method for estimating shuffles results in a
practical solution for the jigsaw puzzle problem. Numerical experiments
demonstrate the competitive accuracy of this solution, its robustness to
corruption and its computational advantage for large puzzles
A reliable order-statistics-based approximate nearest neighbor search algorithm
We propose a new algorithm for fast approximate nearest neighbor search based
on the properties of ordered vectors. Data vectors are classified based on the
index and sign of their largest components, thereby partitioning the space in a
number of cones centered in the origin. The query is itself classified, and the
search starts from the selected cone and proceeds to neighboring ones. Overall,
the proposed algorithm corresponds to locality sensitive hashing in the space
of directions, with hashing based on the order of components. Thanks to the
statistical features emerging through ordering, it deals very well with the
challenging case of unstructured data, and is a valuable building block for
more complex techniques dealing with structured data. Experiments on both
simulated and real-world data prove the proposed algorithm to provide a
state-of-the-art performance
A Global Approach for Solving Edge-Matching Puzzles
We consider apictorial edge-matching puzzles, in which the goal is to arrange
a collection of puzzle pieces with colored edges so that the colors match along
the edges of adjacent pieces. We devise an algebraic representation for this
problem and provide conditions under which it exactly characterizes a puzzle.
Using the new representation, we recast the combinatorial, discrete problem of
solving puzzles as a global, polynomial system of equations with continuous
variables. We further propose new algorithms for generating approximate
solutions to the continuous problem by solving a sequence of convex
relaxations
Detection of Total Rotations on 2D-Vector Fields with Geometric Correlation
Correlation is a common technique for the detection of shifts. Its
generalization to the multidimensional geometric correlation in Clifford
algebras additionally contains information with respect to rotational
misalignment. It has been proven a useful tool for the registration of vector
fields that differ by an outer rotation. In this paper we proof that applying
the geometric correlation iteratively has the potential to detect the total
rotational misalignment for linear two-dimensional vector fields. We further
analyze its effect on general analytic vector fields and show how the rotation
can be calculated from their power series expansions
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