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# Merging

Merging uses bilinear interpolation to determine each frame's contribution to the accumulated image, with each contribution assigned equal weight. Where bilinear interpolation does not define a value, the accumulated image pixel is not updated. Sections below outline the properties of this approach.

## Properties

### Convolution with the Bartlett (triangle) filter as the limiting case

Assuming predicates for translation and point sampling, bilinear interpolation is equivalent to convolution with a Bartlett filter. Combined with the box filter approximation, jittering assumptions, and Bartlett filter approximation, the result of merging should be an acceptable approximation of T. This should be proven at some point. Until then, this result should be considered unreliable.

### Density and false local minima

Informally, the merging method outlined above always updates a dense set of pixels in the accumulated image. In particular, any accumulated image pixel whose center falls on a line between updated pixels is also an updated pixel.

It is conceivable that this property reduces the likelihood of alignment failure due to entrapment in local minima; hence, the merging renderer is always used as a reference for the alignment algorithm. Except in cases where a large radius is used, drizzling does not share these properties.

Copyright 2002, 2003, 2004 David Hilvert

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