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The Registration Algorithm

This section presents the model-based non-rigid registration algorithm in the form of pseudo-code. Initially, the algorithm is demonstrated using simplistic one-dimensional data. The algorithm can be conceptually divided into two parts as follows:

Initialisation

• Generate images or retrieve them from a file.
• Optionally, apply image smoothing.
• Choose image reference. By default, the image closest^5.5 to the mean of all images gets selected.

Main Loop

• For a (pre-defined) number of iterations in the registration:
  • Set the level of precision for the optimiser to reach. Ideally, this level should be increased (or tolerance lowered) when advancements toward the goal are made small, i.e. registration is approached.
  • Repeat for all images:
    • If the current image is not a reference image^5.6:
      • Set up the positions of knot-points (random placements, drawn from a Gaussian distribution, are typically chosen).
      • Given the knot-point positions, apply warps to the current image and seek the warp parameters which minimise the complexity of the model built from the entire set of data.
    • end if
  • end repeat
• end for
• Statistics and registration logging take place.

At the core of this algorithm lies an evaluator of the complexity of the model. The determinant, as characterised in Equation 5.1, is used and shown in experiments that follow. It aligns with the strategy used to build shape models, as described in Chapter 4. Simplicity in computation is particularly important in this case because many models are built and evaluated while optimising.

Figure shows the process which is outlined above. The framework is demonstrated in a simplified form in both cases (schematically and algorithmically). A reference image, as seen at the top of the figure (marked as ``R''), remains unaffected throughout NRR while all other images get manipulated. These are used to construct a model from which the complexity measure can be derived, e.g. an approximation of its description length. Based on that measure of complexity, subsequent warps are applied to the group of images.

Figure: Schematic of the registration algorithm. A reference image (R) and the remainder of the warped set of images (I) form a combined model (represented as a circle), which is evaluated using the objective function to refine subsequent warps.

What follows are some key experiments which investigate the different parameters and pertinent methods used in NRR. Together with corresponding videos (see accompanying CD-ROM), I demonstrate the process of registration - sometimes visually - with an element of progression, i.e. dimension of time. There are also quantitative results.