MAPaint Technical Report:
3D Images

3D Images

The paint program is based on the image processing library known as woolz[8,5,6,4] developed over the years at the MRC Human Genetics Unit. Internally the images are in woolz format which is interval coded and therefore compact for sparse image data and very efficient for the most frequent IP operations required for this program and the gene-expression database, and in particular binary operators - union, intersection, difference; morphological operations - erode, dilate, opening, closing; domain operations - segmentation, labelling, thresholding.

The 3D image structure in woolz is a simple extension of the 2D structure. In 2D an image (one of a number of possible woolz objects) is defined over an arbitrary region of a discrete 2D space with coordinates (k, l) where k is the column coordinate and l the line coordinate. For each line in the image there is a list of intervals which give the start and end points of the image along that line. There is a list (possibly empty) of intervals for each line and it is clear that an arbitrarily complex region of the discrete space can be defined in this way. It is assumed that the discretisation in the x and y directions is at fixed regular intervals, constant in both directions but not necessarily equal. The 3D structure is simply a stack of 2D images again with the constraint that the planes are evenly spaced and that within the plane bounds there must be a 2D image for every plane, although the image could be the empty set. The plane coordinate is defined to be p.

The advantage of the woolz encoding is that only grey-level information within the domain of the image is stored rather than for the whole rectangular box defined by the column, row and plane bounds. For the mouse atlas this can reduce the memory requirements in some cases by about a factor of five which is very significant for the later embryo stages where the grey-level image data may exceed 500 MBytes. Even with woolz encoding we may have to consider some form of lossy compression.

Each reconstruction will have its own internal discrete coordinate system with an associated affine transform which will provide the link between internal coordinates and external, biologically relevent coordinates. Furthermore it is likely that each anatomical component will have its own coordinate frame defined in order to establish the localised meaning of terms such as anterior-posterior . These coordinate systems are not discussed here. The geometry detailed below is entirely within the internal coordinate system and is concerned with how arbitrary sections are presented to the user, how fixed point constraints are imposed on a view, the definitions of the viewing parameters and miscellaneous geometric calculations for example calculating the lines of intersection of views.