1. Planar Orientation from Blur Gradients in a Single Image Scott McCloskey Honeywell Labs Golden Valley, MN, USA Michael Langer McGill University Montreal, QC, Canada

2. Outline Introduction Relation to Previous Work Modelling the Blur Gradient Planar Orientation Estimation Algorithm ◦ Estimating Tilt ◦ Estimating Slant Test Data and Experimental Results

3. Introduction A focus-based method to recover the orientation of a textured planar surface patch from a single image

4. Relation to Previous Work Depth from Defocus Shape from Texture ◦ Distance effect ◦ Foreshortening effect

5. Modelling the Blur Gradient(1/3) The goal of planar orientation algorithms is to accurately estimate the slant and tilt of a 3D plane

6. Modelling the Blur Gradient(2/3) Visible surface is a plane of depth The slant and tilt are the same at all positions in the image patch Focal length : f The distance from the sensor plane to the lens:

7. Modelling the Blur Gradient(3/3) camera’s aperture :F focal length: f sensor distance: blur radius: image position: (x,y) is a linear function of inverse depth blur radius is a linear function of image position (x, y) the blur gradient

8. Planar Orientation Estimation Algorithm(1/3) Image blur is best observed in the middle to high spatial frequencies ◦ remove low frequencies by low pass filter Comparing the blur along different lines in an image ◦ Sharpness measure

9. Planar Orientation Estimation Algorithm(2/3) Estimating Tilt ◦ Equifocal contour  A contour along which the amount of optical blur remains constant ◦ Fnding surface tilt searches for the direction in which the sharpness gradient is maximized

10. Estimating Slant ◦ Slant is estimated as the angle whose back- projection ◦ Produces the smallest gradient in the sharpness measure in the direction of former depth variation ◦ Uniformly blurred image (“doubly blurred image ”) Perspective- induced size change

11. Test Data and Experimental Results(1/4) Test set: 1404 camera images ◦ 9 planar textures ◦ 26 carefully-controlled orientations ◦ 6 different apertures (F = 22, 16, 11, 8, 5.6, 4) 26 planar orientations(Table 1.)

12. Test Data and Experimental Results(2/4) Orientation Estimation Results

13. Test Data and Experimental Results(3/4) Experiments with Image Size

14. Test Data and Experimental Results(4/4) Experiments with Natural Images