Initialized from an approximate linear pairwise alignment that is estimated using local image features, the local vicinity around each vertex is inspected for an optimal match. Candidates are rejected if either r was too low (not similar), there was more than one maximum with very similar r (ambiguous), the maximum is not well localized in both dimensions (an edge pattern that fits everywhere alongside the edge).Ĭorresponding locations are searched through block matching. The candidate for the translational offset is the translation with maximal r. The PMCC coefficent r is grey-coded in the range from -0.7 to 0.7. The above windows display six examples of such correlation surfaces for translations in a square region with the origin in the middle. affine), for each vertex of the spring mesh, an offset is searched calculating the PMCC coefficient r of a block at all possible x,y translations in a given local vicinity over the overlapping image. Starting from an approximate alignment (e.g. 2: Match filter based on the correlation surface. We initialize the system with a linear-per-image optimal pre-alignment based on local image features. The former because the meshes will fold otherwise, the latter to narrow the matching space with the benefit of both, increased speed and better reliability. Linear Initializationīoth relaxing the system of meshes and identifying corresponding locations between images require good initialization. Vice versa, vertices of the target image are connected to their corresponding location in the source image with their `passive’ ends being moved by the respective affine transformation of a source triangle. During simulation, it moves according to the affine transformation defined by the target triangle. This `passive’ end does not contribute to the deformation of the target mesh. The vertex is then connected into the target mesh by a zero-length spring with its target end being located at an arbitrary place in a triangle of the target mesh. The vertices of a triangle define an affine transformation for all pixels in the triangle.įor those vertices of a source image overlapping a target image, we identify its corresponding location in the target image. That is, for all local deformations smaller than the size of a triangle, the mesh will drag towards a rigid transformation. A triangle of springs has two families of cost minima in the plane: 1) at rigid transformations and 2) at rigid transformations flipped. That way, the system penalizes arbitrary warp and distributes the deformation evenly among all images.Įach image is tessellated into a mesh of regular triangles with each vertex being connected to its neighboring vertices by a spring (see Fig. Non-zero length springs within the image preserve each images shape at locally rigid transformation. Zero-length springs connect corresponding locations between two overlapping images and warp the images towards perfect overlap. We achieve this globally minimized deformation by simulating the alignment as an elastic system of spring connected vertices. 1: Triangular section mesh with a resolution of 5 vertices per each long row. Elastic Deformation with Spring Meshesįig. That way, arbitrarily large series of images can be aligned without accumulating artificial warps. The warp for each single image is calculated such that each image in the whole global montage or series will be deformed minimally. Images are warped such that corresponding regions overlap optimally. Incorporates both elastic montaging and elastic series alignment through the alignment menu for series alignment and montaging of large multi-tile section series Montaging mosaics from overlapping tiles where the tiles have non-linear relative deformationĪlignment of deformed section series from serially sectioned volumes The method is accessible through the plugins Elastic Stack Alignment and Elastic Montage and incorporated in the TrakEM2 software. We describe here our elastic alignment method for series or groups of overlapping 2d-images. 7 serial TEM sections of the neuropil of a Drosophila melanogaster first instar larva, downscaled by a factor of 12. Example 1: Example for elastic alignment and montaging.
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