Technion – Electrical Engineering –Software Lab 3D Geometric Objects Search Lyakas Alexander Instructor: Dr. Sigal Ar Given a collection of search objects Given a collection of search objects Find objects that are similar to the search object Find objects that are similar to the search object A user marks some objects as ‘GOOD’ and ‘BAD’ A user marks some objects as ‘GOOD’ and ‘BAD’ Considering user’s feedback Considering user’s feedback
The Workflow ► Gather 3D colored objects from WWW ► Convert them to a single format, convenient for sampling ► Perform sampling: present each object as a set of 3D points, normals to object’s surfaces at these points and the colors of the points ► Correct the directions of the normals, so that all objects have consistent normal directions ► Normalize object’s position, rotation and scale ► Present each object as a numerical vector, AKA ‘feature vector’ ► Perform the testing of the system with real users
Some Theory We can compare them using the (square of) standard Euclidean distance: By adding weights and a bias value we can refine the distance function: Consider two objects represented as feature vectors: Treating the distance as a similarity measure, we sort all the objects according to their distance from the search object. To refine a search, we recalculate the weights and the bias value in order to meet certain constraints.
More Theory – Calculating Features The pqr-th moment in three-dimensional space is defined as: It can be approximated as: Taking object’s colors into account gives three additional coordinates and thus we work in six-dimensional space. Feature vector with third-order moments in three-dimensional space looks like this: The order of the moment is p+q+r We calculated features for different orders, considering and ignoring colors, using the sampled points and normals.
The Search Example The search object is the plane at the top-left corner. Initial search was performed and the feedback has just been given.
The Search Example – Second Iteration Results