Shape Blending


Suppose you are given a set a range data (this is a set of 3D points which are measured from an object's surface using a range scanner). How can you determine a shape which could have resulted in such data? And how concise a description can be provided? An example of this problem is shown in the picture below, which shows a set of range data (left), along with one possible shape model which describes this data (right).

Range data and an extracted shape model

In addition to estimating the shape of the surface from which the data was scanned, it is also worthwhile to keep the description of this surface as precise as possible. Having a short description of an object makes it easier to reason about the object for indexing or recognition.

This process is complicated by data that is noisy, sparse, or incomplete. There is little hope of accomplishing this task without using a model-based approach. In this case, we have developed a shape representation technique called shape blending. Briefly, this representation allows for two shapes to be combined together by "cutting" the desired parts from each, and "gluing" them together.

Having such a representation isn't enough, however, as there must be a robust and efficient method for estimating such a model. The blending representation was carefully tailored for this purpose. Blending allows for the smooth addition of parts and holes to an object. The smoothness of the process keeps the decisions that have to be made during estimation relatively simple.


Below are two experiments showing examples of the automatic estimation of a shape model using the blending representation.

In this first experiment, partial data from a scanned mug, which is shown from two views in (a), is initially fit using an ellipsoid model in (b). Based on automatic analysis of the result, the model is "split" into two in (c). Then, in (d) and (e), the parameters of each part are estimated separately while maintaining a good geometric connection between them (using blending). The model is split again in (f), and this time, a hole is automatically inserted, leading to the final fit in (g). This repeated application of blending also leads to a qualitative model description in (h) (the labels in the boxes are hand generated). About 70 shape parameters were needed to describe this mug.
Estimation of a mug

This second experiment involves generated (artificial) data from a two-holed object, shown in (a). It is used to demonstrate the process of blending on a more topologically complex object. As before, after an initial ellipsoid fit in (b), the model is split and re-fit several times in (c) through (f) to reach the final fit in (g). 84 shape parameters were required to describe this object.
Estimation of a two-holed box


There are a number of available on-line publications describing this work (in chronological order):