scholarly journals Accurate Closed-form Estimation of Local Affine Transformations Consistent with the Epipolar Geometry

2016 ◽  
Author(s):  
Daniel Barath ◽  
Jiri Matas ◽  
Levente Hajder
Keyword(s):  
Closed Form ◽  
Epipolar Geometry ◽  
Affine Transformations

2-D Affine Transformations Cannot Account for Human 3-D Object Classification

Perception ◽  
1997 ◽  
Vol 26 (1_suppl) ◽  
pp. 241-241
Author(s):  
Z Liu
Keyword(s):  
Object Recognition ◽  
Closed Form ◽  
Human Performance ◽  
Structural Information ◽  
Image Plane ◽  
Ideal Observer ◽  
Affine Transformations ◽  
Statistical Efficiency ◽  
Linear Transformations ◽  
Radial Basis

Converging evidence in object recognition has shown that the performance of human observers depends on their familiarity with the appearance of the objects. The degree of this dependence is a function of the inter-object similarity in the object set. The more similar the objects are, the stronger is this dependence, and the more dominant is two-dimensional (2-D) image information. However, the extent to which 3-D structural information is used still remains an area of strong debate. Previously, we showed that all models that allowed 2-D rotations in the image plane of independent 2-D templates were unable to account for human performance in recognising novel object views. Here we derive a closed-form Bayesian ideal observer that gives rise to probably the best possible performance when applying 2-D affine transformations (translation, rotation, scaling, stretching, and other linear transformations) to stored 2-D templates. In addition, we compare human performance with a closed-form derivation that finds the best match between a 2-D template and a 2-D image under 2-D affine transformations. We also compare human performance with a generalised radial basis functions model. This model establishes optimal performance for learned 2-D templates, and then adjusts the variance of its radial basis (Gaussian) functions to achieve best possible performance for novel views of individual objects. We demonstrate that none of these models can account for human performance in 3-D object recognition. Human statistical efficiency for novel views is higher than for learned views, which suggests that 3-D structural information is used by human observers.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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