Current Research Topic
First order tensor voting, and application to scale inference
( Wai-Shun Tong, Chi-Keung Tang, Gerard Medioni )


Many computer vision asysmtes depend on reliable detection of 3-D boundaries and regions in order to proceed. In the prsence of outliers, missing data, and orientation discontinuities due to occlusion, it is difficult to detect boundaries and interpolate data without over-smoothing important feature curves. In this paper, we address these problems by incorporating first order tensor information into the tensor voting formalism, which is second-order based. To propagate an adaptive smoothness constraint at a preferred orientation non-iteratively, we vote for a first order tensor (or vector) to capture polarity and orientation information. To integrate first and second order tensors, we propose an algorithm for inferring the proper scale based on the continuity constraint, and to preserve the finest details. Given a noisy 3-D point set, the new and improved formalizm can better localize boundary curves and orientation discontinuities. Unlike many approaches that over-smooth features, or delay the handling of boundaries and discontinuities until model misfit occurs, the interaction of smooth features, boundaries, discontinuities, outliers are encoded at the representation level. We show results from a variety of datasts to show the efficacy of the improved formalism.


Demonstration of multiple scale features extraction.
3D data points with noise before surface extraction

result of the surface extraction with small scale of analysis

result of the surface extraction with large scale of analysis

Demonstration of detection of endcurve, from stereo reconstructed depth map
Stereo Pair of the "Renault"

reconstructed depth map and the inferred endcurve marked as red

Experimental results on 12 CT scan of the Thorax dataset.
3 slices of the CT scans showing the inferred boundaries of the thorax (the red curves)

3D boundary points before surface extraction

To show our approach is noise insensitive, we added one part of random noise

result of the surface extraction (mpeg movie)

Experimental result on the McGill Brain dataset.
(Sagittal) CSF boundary (Transveral) CSF boundary (Coronal) CSF boundary

(Sagittal) Gray Matter boundary (Transveral) Gray Matter boundary (Coronal) Gray Matter boundary

(Sagittal) White Matter boundary (Transveral) White Matter boundary (Coronal) White Matter boundary

Sagittal Refined Cortex boundary Transveral Refined Cortex boundary Coronal Refined Cortex boundary
The inner cortical surface (shown in blue), and the outer cortical surface (shown in red)

(Sagittal) Inner Cortical Surface (Transveral) Inner Cortical Surface (Coronal) Inner Cortical Surface
result of Inner Cortical the surface extraction (mpeg movie)

(Sagittal) Outer Cortical Surface (Transveral) Outer Cortical Surface (Coronal) Outer Cortical Surface
result of the Outer Cortical surface extraction (mpeg movie)