Sparse Coding under Occlusions: Individual TreeSegmentation in Remote Sensing

Xiaohao Cai

Department of Applied Mathematics and Theoretical Physics (DAMTP)University of Cambridge

withD. Coomes, J. Lee, J. Lellmann, C.-B. Schonlieb

Challenges in Dynamic Imaging Data

June 09–11, 2015

Object detection

Synthetic Synthetic Synthetic

Coin Apple Tree CHM of LiDAR

Sparse coding model - original

minv∈RN

{λ‖v‖1 + ‖

∑Ni=1 viei − f ‖22

}

I Given image f ∈ RM1×M2

I Regularisation parameterλ > 0

I Library E = {e1, . . . , eN},where ei ∈ RM1×M2

I Coefficient vectorv = (v1, . . . , vN)> ∈ RN

I ‖ · ‖1 – enforces sparserepresentation of v

ei ∈ Evi 6= 0vi = 0

Sparse coding model - extended

minv∈RN

{λ‖v‖1 + ‖

∑Ni=1 viei − f ‖22

}given image

�

@@Rextended

I Fail under occlusion case

I No parallelism

∑Ni=1 viei

HHY

vHHY

I Work under occlusion case

I Parallelism

new∑N

i=1 vieiHHY

new vHHY

Preliminary results

Given apple image Our result Our v - object position

Given tree CHM Our result Our v - object position

Conclusions

Aim

I Tree segmentation fromremote sensing data – largedata

I Sparse coding underocclusions method

I Parallel computation

Challenging aspects

I Proper library (E ) selection

I Robust and goodperformance

I Automatic software toolbox

THANK YOU!