Active Flattening of Curved Document Images via Two Structured Beams Gaofeng MENG*, Ying WANG, Shenquan QU Shiming XIANG, Chunhong PAN National Laboratory of Pattern Recognition (NLPR) Institute of Automation, Chinese Academy of Sciences (CASIA)

The problem Document images, e.g., an opened book image, captured by a digital camera often get distorted … Images come from Baidu.com

Our objective Distorted image Corrected result origninal corrected binarized binarized

Related work Text-lines based methods Multiple views based methods Extraction and fitting of curved text-lines in high accuracy is very challenging Fail to images with sparse text-lines or no text-lines. Multiple views based methods Feature points matching may fail to areas with large distortion Contents dependent Methods using range data Computation expensive, sometimes instable Some physical methods V-bed or V-head scanner, not a contactless method, not suitable for fragile documents

ONE digital camera +TWO laser light sources Our designed system ONE digital camera +TWO laser light sources

Main features Simple and fast High accuracy Image contents independent Main components consist of One camera and two lasers Dewarping has a closed-form solution High accuracy Average dewarping errors less than 0.3mm Image contents independent Independent of document contents More general shape assumption Suitable for pages with developable shape Fully automatic Non-parametric, one-button operation Working in a non-contact manner

3D directrices estimation Developable surface interpolation How it works? 3D directrices estimation Developable surface interpolation Surface flattening Image dewarping Input images Output images ① ② ④ ③

3D directrices estimation Camera and beams calibration Using checkerboard patterns Beams extraction Capturing two images with and without beams Beams can be easily located in the difference map

Developable surface interpolation - One 3d directrix - The other 3d directrix - The correspondence A ruled surface is developable if and only if

Developable surface interpolation Thus, developable surface interpolation turns out to be finding a correspondence function so that the developable condition is satisfied. - One 3d directrix - The other 3d directrix - The correspondence A ruled surface is developable if and only if

Solving the variational problem Discritize the t-s plane and construct a directed weighted graph according to the given constraints. The problem finally becomes finding a shortest path from (0,0) to (1,1) on the graph.

Surface flattening A developable surface can be flattened by unrolling its two directrices. This can be done by using the invariance property of geodesic curvature of a curve on the developable surface.

Geodesic curvature What is the geodesic curvature? For a curve on a surface, its curvature vector can be divided into two components: Invariance of geodesic curvature When a developable surface is flattened, the geodesic curvature will remain unchanged.

Flattening a curve on the surface A curve on the surface can be flattened by solving the following ODEs - the geodesic curvature of the curve to be flattened - the starting position of flattening - the direction of flattening at the starting point

Solving the ODEs The above ODEs have closed-form solutions:

Image dewarping Once the developable surface is flattened, we actually establish a dewarping transformation. This transformation is then applied to the input image to correct its geometric distortion.

Experimental results Here are some results

More results

Quantitative evaluation

Conclusions A practical system for geometric correction of captured document images Using two active structured beams Developable surface assumption Image contents independent Simple, fast and fully automatic