CMU thesis proposal: Scale Selection and Invariance in Low Level Vision

Ranjith Unnikrishnan, Robotics Institute
18 Sep 2006

The representation of objects through locally computed features is a concept common to many approaches in 2-D and 3-D computer vision. The use of local information to infer global properties aims to serve several purposes such as robustness to outlying structures, variation in viewing conditions, noise and occlusion. Reliable computation of relevant local attributes is thus an important part of any practical vision system intended to perform higher level reasoning.

The task of making such local observations necessitates making choices of the neighborhood size within which the computation is performed, also referred to as the /scale/ of the observation. This in turn poses several unanswered questions relevant to both data representation (e.g. reconstruction and compression) as well as data identification (e.g. object detection and classification). At what scale is it meaningful to compute a local feature? What is the optimal neighborhood size for estimating local geometric properties from data? While many advances have been made in a theory of scale for 2-D luminance images, little attention has been paid to the domains of unorganized point clouds (as would be acquired with a laser range scanner) or to alternate representations of images (such as color or other pixel-wise functions such as optical flow).

This thesis explores the problems of scale selection and invariance in previously unaddressed problem domains, and proposes solutions for several useful vision tasks:

* We propose to extend current application of scale theory for interest region extraction in 2-D images to alternate, potentially more useful representations. As an example, we demonstrate how both scale as well as illuminant invariant keypoint detection may be achieved in the case of color (RGB) images without having to estimate the properties of the illuminant.

* We present methods to robustly compute local differential properties from non-uniform unstructured point clouds. In particular, we show how data-driven adaptation of the neighborhood size in local PCA when computing tangents (normals) from spatial curves (surfaces) can make even this naive estimator more robust than leading fixed-scale alternatives.

* We propose the development of new scale-space representations of 3-D point cloud data that are robust to changes in sampling. By this, we advocate changing the current practice of using a single globally fixed value of scale when computing shape descriptors from 3-D data to that of using a value that is locally data-driven.

* We propose to investigate the application of local intrinsic scale detection for manifold learning. The aims of this analysis are improved statistical properties and robustness of embedding functions and regularizers to sampling variations in the dataset.

Overall, the expected contributions of this thesis are new technique and tools for the scale selection problem that is fundamental to local data analysis and learning from real-world measurements.

Further Details: A copy of the thesis proposal document can be found at the link.