Research: Volume Integration
Figure 1: Alignment of two substacks using projections PZ (A,B) to constrain the (x,y) coordinates, and PY (C,D) to constrain the z coordinate. Red square in the upper (A,B) and lower (C,D) corners indicates the origin of each projection. C: To align in the XZ plane, projections PY(A) and PY(B) need only be aligned in the Z direction. D: The 3D alignment is complete.
We have developed a Volume Integration and Alignment System (VIAS) to create a single volume from multiple 2D image stacks, each of variable dimensions. Realtime alignment of large volumes is possible by defining a workspace in memory, in which 2D projections of all subvolumes can be manipulated interactively. Alignment and integration proceed as a two-step process: (1) alignment of the workspace; and (2) volume integration.
The 3D data are projected along the X,Y and Z axes. Corresponding to each element (x,y,z) in the 3D volume is an intensity or greyscale value. For each pixel in the projection arrays, a sequence of intensity values respectively, is generated from consecutive points along the projection axis, in the direction orthogonal to the projection plane.
For any two adjacent stacks, only two of the planar projections are used for alignment (Fig. 1). Alignment is performed interactively on pairs of projections with click and drag tools inside the VIAS graphical user interface (GUI). The user manually positions adjacent projections into approximate alignment with the mouse (Fig. 1A), then uses the auto-align feature to fine-tune the adjustment (Fig. 1B). This procedure is repeated sequentially with all adjacent projections until the entire object is reconstructed.
Manual selection of the optimal placement of a projection is tedious and error-prone, so an autoalignment feature, initiated from the VIAS toolbox, fine-tunes the adjustments in each plane. The autoalignment algorithm minimizes the scaled norm of intensity differences computed on a subset of the overlapping pixels within a predefined search window around the initial guess from the manual alignment.
Figure 2: Volumetric rendering of reconstructed dendritic segments from 2 substacks following alignment and integration with VIAS system. The integrated volume shows excellent alignment in all three dimensions.
The 3D extent of the volume is computed by taking upper and lower bounds of the aligned workspace along each of the X,Y, and Z axes. Subvolumes are then sequentially inserted into an integrated image at each z-level which is written to disk to construct the integrated volume. For inserted pixels that overlap in-place pixels, either simple replacement by the inserted value, replacement with the maximum of inserted and in-place values or replacement by the average of inserted and in-place values can be implemented.
Because the alignment and integration are performed on 2D projections rather than the volumetric data, the system is extremely efficient and can be run on a standard desktop workstation.