Content-Aware-Rotation

Reproduction of Kaiming He's Paper Content-Aware Rotation on ICCV 2013.
I just test this project on Windows 10, there may be something wrong on Linux system.

Contents

Rotation Manipulation

suppose that :
,
then we have :

further, we can get the derivative :
Line Preservation

suppose that :
,
then we have :

further, we can get the derivative :
Shape Preservation

suppose that :
,
then we have :

further, we can get the derivative :
Boundary Preservation

further, we can get the derivative :
Optimization
Step 1 : Fix θ solve for V
Sparse Linear System :

V is the minimum point of total energy above, thus, let :

we can get the solution for V.
Step 2 : Fix V solve for θ
Part 1 : Fix Φ, update θ

suppose that :

we have :

then let :

by solving a sparse linear system, we can get the solution of θ :

Part 2 : Fix θ, update Φ

the solution of Φ can be easily approximately reached by enumeration based on iteration methods(increase β gradually).

How to Use : download the whole project and run main.py
folder ep : images which are used for formula derivation and some results.
folder image : images which are used in original paper.
folder lsd : line segment detection algorithm in python version.
warp_mesh.py : image warping method realized by embedded function in tensorflow.