Local image structures and optic flow estimation

Abstract

Different kinds of local image structures (such as homogeneous, edge-like and junction-like patches) can be distinguished by the intrinsic dimensionality of the local signals. Intrinsic dimensionality makes use of variance from a point and a line in spectral representation of the signal in order to classify it as homogeneous, edge-like or junction-like. The concept of intrinsic dimensionality has been mostly exercised using discrete formulations; however, recent work (; ) has introduced a continuous definition. The current study analyzes the distribution of local patches in natural images according to this continuous understanding of intrinsic dimensionality. This distribution reveals specific patterns than can be also associated to local image structures established in computer vision and which can be related to orientation and optic flow features. In particular, we link quantitative and qualitative properties of optic-flow error estimates to these patterns. In this way, we also introduce a new tool for better analysis of optic flow algorithms.

keywords:

• Optic flow
• intrinsic dimension
• image structures

Notes

1. For convenience, intrinsic dimension of zero, intrinsic dimension of one, intrinsic dimension of two and intrinsic dimensionality (and intrinsic dimension) will be called i0D, i1D, i2D and iD, respectively, in the rest of the paper.

2. Note that a continuous interpretation can be derived also from the structure tensor (Jähne 1997) by computing origin and line variance using the two eigenvalues.

3. In our simulations, we used the standard values 0.5 and 1.0 for α and δ, respectively, as suggested and usually practiced in the literature (see, e.g., Barron et al. (1994)).

4. We also analyzed the distribution of magnitude, but as expected found no dependence on the intrinsic dimensionality (for details, see Kalkan et al. (2004)).

5. Each image contains 44 × 1440 measurements with an angular separation of 0.18 degree. The field of view is 80 degree vertically and 259 degree horizontally. The distance of each point is calculated from the time of flight of the laser beam, where the operational range of the sensor is 2–200 m. The laser wavelength of the laser beam is 0.9 μm in the near infrared region.

6. We also made measurements using angular and magnitudal errors with the formulas , respectively. However since they show similar patterns they are not shown in this paper (for details, see Kalkan et al. (2004)).