FR3.L09 - MULTIBASELINE GRADIENT AMBIGUITY RESOLUTION TO SUPPORT MINIMUM COST FLOW PHASE UNWRAPPING
1. Multibaseline gradient ambiguity resolution to support Minimum Cost Flow phase unwrapping Marie Lachaise, Richard Bamler, Fernando Rodriguez Gonzalez Remote Sensing Technology Institute, DLR
2.
3.
4.
5. Some gradient pdfs 0 2 -2 1 2 3 Gradient in azimuth (rad) pdf 0 2 -2 0.5 1 1.5 Gradient in range (rad) pdf
6. Which additional information can we use ? curl(i,k) = i (i,k)+ k (i+1,k) - i (i,k+1)- k (i,k)=0 (i,k) (i+1,k) (i+1,k+1) k (i+1,k) i (i,k)+ k (i+1,k) - i (i,k+1)- k (i,k)=0 (i,k+1) i (i,k) i (i,k+1) k (x,y) (x,y+1) Phase pixels Gradient estimates Zero-curl constraint
7.
8. Maximum A Posteriori and energy minimization Data energy or data penalty Compatibility between neighboring variables
9. Graphical model Gradient estimates Observable variable node Function node Pdf (hidden | observation) Zero-curl constraint check nodes Hidden variable node = unknown true values of gradients = gradient node Partial derivative over range Partial derivative over azimuth Phase value Gradient node Measured gradient Constraint node
10.
11. Message update: from constraint node to gradient node m 4 Gradient node Constraint node m 1 m 2 m 3
12. Messages update: from gradient node to constraint node m 4 m 5 Gradient node Constraint node
For multichannel, where different noisy scaled wrapped measures are available the ML function of the phase measure exhibits a „unique“ peak or at least „less ambiguous“ maxima. MLE eliminates or at least mitigates the ambiguity problems related to the wrapping operator but it has the disadvantage to amplify the noise contribution during disambiguation process.
The max product BP algorithm works by passing messages around the graph defined by the four connected image grid.
![Outline ,[object Object],[object Object],[object Object],[object Object],[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)