Guidance systems designed for neurosurgery, hip surgery, and spine surgery, and for approaches to other anatomy that is relatively rigid can use rigid-body transformations to accomplish image registration. These systems often rely on point-based registration to determine the transformation, and many such systems use attached fiducial markers to establish accurate fiducial points for the registration, the points being established by some fiducial localization process. Accuracy is important to these systems, as is knowledge of the level of that accuracy. An advantage of marker-based systems, particularly those in which the markers are bone-implanted, is that registration error depends only on the fiducial localization error (FLE) and is thus to a large extent independent of the particular object being registered. Thus, it should be possible to predict the clinical accuracy of marker-based systems on the basis of experimental measurements made with phantoms or previous patients. This paper presents two new expressions for estimating registration accuracy of such systems and points out a danger in using a traditional measure of registration accuracy. The new expressions represent fundamental theoretical results with regard to the relationship between localization error and registration error in rigid-body, point-based registration. Rigid-body, point-based registration is achieved by finding the rigid transformation that minimizes "fiducial registration error" (FRE), which is the root mean square distance between homologous fiducials after registration. Closed form solutions have been known since 1966. The expected value (FRE2) depends on the number N of fiducials and expected squared value of FLE, (FLE-2, but in 1979 it was shown that (FRE2) is approximately independent of the fiducial configuration C. The importance of this surprising result seems not yet to have been appreciated by the registration community: Poor registrations caused by poor fiducial configurations may appear to be good due to a small FRE value. A more critical and direct measure of registration error is the "target registration error" (TRE), which is the distance between homologous points other than the centroids of fiducials. Efforts to characterize its behavior have been made since 1989. Published numerical simulations have shown that (TRE2) is roughly proportional to (FLE2)/N and, unlike (FRE2), does depend in some way on C. Thus, FRE, which is often used as feedback to the surgeon using a point-based guidance system, is in fact an unreliable indicator of registration-accuracy. In this work we derive approximate expressions for (TRE2), and for the expected squared alignment error of an individual fiducial. We validate both approximations through numerical simulations. The former expression can be used to provide reliable feedback to the surgeon during surgery and to guide the placement of markers before surgery, or at least to warn the surgeon of potentially dangerous fiducial placements; the latter expression leads to a surprising conclusion:...

SummaryIn Drosophila, ∼50 classes of olfactory receptor neurons (ORNs) send axons to 50 corresponding glomeruli in the antennal lobe. Uniglomerular projection neurons (PNs) relay olfactory information to the mushroom body (MB) and lateral horn (LH). Here, we combine single-cell labeling and image registration to create high-resolution, quantitative maps of the MB and LH for 35 input PN channels and several groups of LH neurons. We find (1) PN inputs to the MB are stereotyped as previously shown for the LH; (2) PN partners of ORNs from different sensillar groups are clustered in the LH; (3) fruit odors are represented mostly in the posterior-dorsal LH, whereas candidate pheromone-responsive PNs project to the anterior-ventral LH; (4) dendrites of single LH neurons each overlap with specific subsets of PN axons. Our results suggest that the LH is organized according to biological values of olfactory input.

Abstract-A sequential algorithm is presented for computing the exact Euclidean distance transform (DT) of a k-dimensional binary image in time linear in the total number of voxels N. The algorithm, which is based on dimensionality reduction and partial Voronoi diagram construction, can be used for computing the DT for a wide class of distance functions, including the L p and chamfer metrics. At each dimension level, the DT is computed by constructing the intersection of the Voronoi diagram whose sites are the feature voxels with each row of the image. This construction is performed efficiently by using the DT in the next lower dimension. The correctness and linear time complexity are demonstrated analytically and verified experimentally. The algorithm may be of practical value since it is relatively simple and easy to implement and it is relatively fast (not only does it run in OðNÞ time but the time constant is small). A simple modification of the algorithm computes the weighted Euclidean DT, which is useful for images with anisotropic voxel dimensions. A parallel version of the algorithm runs in OðN=pÞ time with p processors.