Author: Park
Year: 2017
- photometric cost is based on brightness consistancy assumption
- evaluation of lighting change robust pose estimation method
Direct Image alignement:
- look at the robustness of photometric residual in isolation
- Uses RGB-D images to ignore the depth estimation pb
- Pb: an image
$I$ , with a depth map$D$ needs to be aligned with a template$T$ . We need to find the transformation$\mathbf{M}$ that warps every pixels$x$ with depth$d$ on$T$ : $$ W(x, d, \mathbf{M}) = \pi_T \ (\mathbf{M} . \pi^{-1}I (x, d)) $$ Thus the image alignement pb can be formulated as: $$ C(\mathbf{M}) = \frac{1}{\Omega} \sum{x \in \Omega} \rho(T(W(x,d,\mathbf{M})) - I(x))) $$ - Dense descriptor images can be used as well
$D_T$ and$D_I$ the pb is then $ \begin{equation} C(\mathbf{M}) = \frac{1}{\Omega} \sum_{x \in \Omega} \rho(D_T(W(x,d,\mathbf{M})) - D_I(x))) \end{equation} $ - But do we compute the descriptors on the original image or on the warped image?
Robust Formulation:
- Global median bias normalization (GMedian): (1) is normalized by the median of the residuals
- Global affine model: intensities of one image are transformed by an affine function
$I(x) = (1+\alpha)I(x) + \beta$ , each iteration jointly optimize$\Delta \mathbf{M}, \delta \alpha, \delta \beta$ - Zero Mean Normalized Cross Corelation: maximises ZNCC for image alignement
- Mutual information: compute MI on the occurence probability of intensities
- Gradient Magnitude: align gradient magnitude instead of image intensities (descriptor based method)
- Local mean bias normalization: locally normalizes pixel intensities by substracting from them the mean intensity of a patch around them (descriptor based method)
- Descriptor Field: compute a descriptor image using convolutions
- Census Transform: binary descriptor based on intensity comparison (classic) (descriptor based method)
Evaluation:
- the testing is performed frame to frame
- metric: drift in cm/second
- methods convergence probabilities facing rotation, translation and illuminatino change on synthetic data: Brightness Consistency Assumption (BCA) fails for small illumination changes
- BCA is the fastest in runtime performance, all implementations are run on GPU
- Direct method better to refine pose, Indirect (SIFT) better for large changes