To the Graduate Council: I am submitting herewith a dissertation ...

Chapter 3: A Feature Saliency Descriptor for Registration and Pose Recovery 34Table. 3.7. Variation of NSwithas the quality of the reconstruction degrades ( ϕ : correct rotation).ϕx: the number of salient points will decrease significantly0x0ϕxϕxϕ + 20x0ϕ + 40x0ϕ + 60x0N 1930 858 425 224SWe recall that in the 2D case the voting process for a point-set P is performed using astick field, which encodes unit vectors pointing from one siteXiT= ( x , y ) ∈ P toiianother siteXjT= ( x , y ) ∈ P where the vote is being cast. Following thejjformalism described in [Medioni00] the unit vector pointing from the first site to thesecond (indexed i and j)X − Xt )X − Xrepresentation using the covariance matrix of equation (3.8).ij i j ij ij T= = ( tx, tyis encoded in tensorijij 2 ij ij⎡(t ⎤x) txtyTij= ⎢ ij ij ij 2⎥(3.8)⎢⎣txty( ty) ⎥⎦1+ ( y2⎡ ( xi−xj)⎢⎢⎣( xi−xj)(yi− y( x −x)( y= i j i22( x − ) − )) ( − )2ixj iyjjyiyj− yj) ⎤⎥⎥⎦As we mentioned above the strength of the votes is made to decay exponentially withdistance. This decay is controlled by a parameterσ , which is related to the scale of the