Computer Vision @ LEMS

Third Order Edge Detector

The traditional approach to edge detection (e.g. canny) using image derivatives localizes edges at the maxima of the gradient magnitude |grad I| in the direction of the gradient grad I/|grad I|, which gives grad(|grad I|) . grad I/|grad I| = 0. In Cartesian coordinates, this condition can be written as F(x,y) = Ix^2*Ixx + 2*Ix*Iy*Ixy + Iy^2*Iyy = 0, which involves up to second-order derivatives. However, the edge orientation is simply taken as the orthogonal to the image gradient, which only involves first order derivatives. This is why the orientations of the edges as computed by the gradient operator are incorrect. The tangent computation needs to involve one higher order gradient than the computation to localize the edges. Hence it needs to involve third-order derivatives. The tangent to the edge contour can be correctly computed by the gradient of F(x,y) at the zero level set. The orientation of the edge thus involves up to third-order derivatives. For this reason we have chosen to call our edge detector the "Third-order orientation detector". In the image above, edgels computed by the traditional method (in red) are compared to those computed by the third-order orientation operator (in green). Notice the consistency of the third-order edges with respect to the edge curves.

Euler Spiral Construction

This software reduces the construction of an Euler spiral from a pair of points and tangents at these points to solving a nonlinear system of equations involving Fresnel Integrals whose solution relies on optimization from a suitable initial condition constrained to satisfy given boundary conditions. Since the choice of an appropriate initial curve is critical in this optimization, an optimal solution is analytically derived in the class of biarc curves, which is then used as the initial curve. The resulting interpolations yield intuitive interpolation across gaps and occlusions, and are extensible, in contrast to the scale-invariant version of elastica.

Edge-Based Figure-Ground Segregation of Moving Objects in Videos from Stationary Camera

This software is an approach to ”background modeling” of a time sequence of images acquired from a stationary camera. The approach is based on sub-pixel edge maps in contrast to the traditional intensity-based background modeling, and is motivated by the observation that intensity-based background models are sensitive to sudden changes in illumination and camera parameters, e.g., gain control. It is shown that the sub-pixel edgemaps show greater robustness to such changes and furthermore, require far fewer training images than comparable intensity-based models, even when sudden illumination changes are not an issue. In addition, in intensity based background models the false positive rate of classifying a foreground pixel as background is high due to the frequent accidental alignment of figure intensities with the background model. In contrast, background models based sub-pixel edge maps are highly localized and specific in orientation. They face a figure-ground ambiguity much less frequently due to the reduced likelihood of accidental alignment. The software models the sub-pixel edge position and orientation using a Mixture of Gaussians model without requiring a higher resolution discretization grid. It has been tested on a wide range of videos and the resulting background models result in a much more selective figure-ground segregation and are easier to train. When you download the package, please read 'installation_steps.txt' and then 'bg_modeling.txt'.

Segregation of Moving Objects Using Elastic Matching

This is a method for figure-ground segregation of moving objects from monocular video sequences. The approach is based on tracking extracted contour fragments, in contrast to traditional approaches which rely on feature points, regions, and unorganized edge elements. Specifically, a notion of similarity between pairs of curve fragments appearing in two adjacent frames is developed and used to find the curve correspondence. This similarity metric is elastic in nature and in addition takes into account both a novel notion of transitions in curve fragments across video frames and an epipolar constraint. Color/intensity of the regions on either side of the curve is also used to reduce the ambiguity and improve efficiency of curve correspondence. The retrieved curve correspondence is then used to group curves in each frame into clusters based on the pairwise similarity of how they transform from one frame to the next. Results on video sequences of moving vehicles show that using curve fragments for tracking produces a richer segregation of figure from ground than current region or feature-based methods. When you download the package, please read 'installation_steps.txt' and then 'curve_tracking.txt'.

Binary Shape Databases

The 99-Shape Database

The 216-Shape Database

The 1070-Shape Database

Brown Extended ETHZ Shape Dataset 

Please visit the following page: http://vision.lems.brown.edu/datasets/brown-ethz