multivew cost funciton

 Multi-view cost functions are used in multi-view stereo (MVS) and multi-view learning algorithms to aggregate information from multiple views or data sources. The cost function typically aims to optimize the matching or reconstruction process across different views.

Key Components of Multi-view Cost Functions

1. Photo-consistency: This measures the similarity of corresponding pixels or features across different views
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2. Spatial regularization: This enforces smoothness and coherence in the reconstructed 3D geometry or learned representations
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3. View aggregation: Costs from individual views are combined, often using weighted sums or other fusion strategies
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Examples of Multi-view Cost Functions

1. MVS Cost Aggregation:
   $S(p,j)={\sum }_i{w}_i(p)\cdot S_i(p,j)$
   Where $S(p,j)$ is the aggregated cost for pixel $p$ at depth hypothesis $j$, $w_i(p)$ is the weight for view $i$, and $S_i(p,j)$ is the cost from view $i$
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2. Multi-view Tracking Cost:
   $c_{i_1{i}_2\mathrm{.}\mathrm{.}\mathrm{.}{i}_N}=-\ln \frac{p(Z_{i_1{i}_2\mathrm{.}\mathrm{.}\mathrm{.}{i}_N}\mathrm{\mid }a)}{p(Z_{i_1{i}_2\mathrm{.}\mathrm{.}\mathrm{.}{i}_N})}$
   This cost function compares the likelihood of measurements belonging to an object versus being false positives
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3. Multi-view Learning Reconstruction Error:
   ${\sum }_{i=1}^n\mathrm{\mid }\mathrm{\mid }{x}_i-g(v_i)\mathrm{\mid }{\mathrm{\mid }}_F^2+{\sum }_{i=1}^n\mathrm{\mid }\mathrm{\mid }{v}_i-f(x_i)\mathrm{\mid }{\mathrm{\mid }}_F^2$
   Used in auto-encoders to minimize reconstruction error across multiple views
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Multi-view cost functions often incorporate terms for data fidelity, regularization, and view consistency. They are designed to leverage complementary information from different views while handling challenges such as occlusions and varying viewpoints.