Creating Generative Models from Range Images


Ravi Ramamoorthi

Computer Graphics Laboratory
Stanford University

Abstract

We describe a new approach for creating concise high-level generative models from range images or other methods of obtaining approximate point clouds. Using a variety of acquisition techniques and a user-defined class of models, our method produces a compact and intuitive object description that is robust to noise and is easy to edit. The algorithm has two inter-related phases---recognition, which chooses an appropriate model within a user-specified hierarchy, and parameter estimation, which adjusts the model to fit the data as closely as possible. We give a simple method for automatically making tradeoffs between simplicity and accuracy to determine the best model within a given hierarchy. We also describe general techniques to optimize a specific generative model that include methods for curve-fitting, and which exploit sparsity. Using a few simple generative hierarchies, that subsume many of the models previously used in computer vision, we demonstrate our approach for model recovery on real and synthetic data.

Summary

It has recently become possible to acquire reasonably accurate point-clouds or range data from 3D objects. For graphical applications, these point-clouds are usually transformed into polygonal meshes or spline patches. However, these representations are difficult to manipulate, and require a large amound of data. Computer vision approaches can recover models from sparse range data. However, these methods are usually restricted to specific, fairly simple models.

By using general algebraic models-the generative models proposed by Snyder-we are able to subsume many of the previous approaches in computer vision and recover high-level models from incomplete range data.

Benefits of our approach:

  • Simplicity: Simple range data acquisition methods including that of Bouguet and Perona are used.
  • Robustness: Because the approach is model-based, we can use incomplete and noisy range data as opposed to some mesh-based methods.
  • Compactness: Savings of two orders of magnitude and more in storage.
  • Intuitiveness: Easy to edit. Parameters are logical model features.

Algorithm

The input to our algorithm beside the range data is an input model class or hierarchy including an algebraic model description from which the model can be evaluated, constraints on curves in the final model, and code for an initial guess for the root model of the hierarchy. The system chooses the appropriate model within the hierarchy and optimizes the parameters as follows:
  1. Acquire Range Data
  2. Fit root model to data
  3. Fit children
  4. Reset model to child with minimal cost and go to step 3 if that improves total cost. Otherwise, exit to step 5.
  5. Refine curves further
  6. Smooth model to prevent overfitting
Steps 2-4 constitute the greedy recognition phase where an appropriate model is chosen from those encoded by the input hierarchy.

Results

These illustrate some of our results. More information will be found in the paper. Clicking on each of these figures will bring up a high-resolution version.

Figure 1 A scene made of several generative models. The models were each recovered from actual range data using a few simple model hierarchies, and then composed. A smooth compact representation was generated despite noisy and incomplete data.

Figure 2 A comparison of the original and recovered models for some of the objects in Figure 1.

Figure 3 Recognition tree for a banana model showing the order in which curves are added.

Figure 4 Comparison of fitting generative models and superquadrics.

Figure 5 An example of using the wrong input hierarchy-one that doesn't have the necessary degrees of freedom to model the data. The left images are of the banana and bowl recovered using the spoon hierarchy while the rotating generalized cylinder is used in the last two to recover the ladle and spoon. We see the algorithm still does the best it can, capturing some of the dominant aspects of the shapes.

Figure 6 Generative models allow for easy, intuitive editing, for instance, of a spoon into a ladle.

Relevant Links

Siggraph 99 paper, Creating Generative Models from Range Images by Ravi Ramamoorthi and James Arvo
pdf (1.5M), postscript (2.5M), high-res pdf (9M), high-res ps (29M)

FTP site for all the material on the CDROM

Figure 1. A scene made of generative models recovered from actual range data


Figure 2. Comparison of the range data (top) with the recovered models (bottom) for the objects in the scene in figure 1.

Figure 3. Comparison of the range data (top) with the recovered models (bottom) for the objects in the scene in figure 1.

Figure 4. Comparison of a superquadric fit (left) with the banana model (right), demonstrating the benefit of generative models over commonly used vision primitives.

Figure 5. Using the wrong model hierarchy for the banana, bowl, ladle and spoon. The algorithm still produces a simple model that mimics the original object to the extent possible.

Figure 6. Generative models allow for easy editing. A recovered spoon (left) is edited intuitively to give a ladle-like shape (right)
Ravi Ramamoorthi
Last modified: Wed Mar 15 19:41:34 PST 2000