Planar Orientation from Blur Gradients in a Single Image

Scott McCloskey

Honeywell Labs

Golden Valley, MN, USA

Michael Langer

McGill University

Montreal, QC, Canada

OutlineIntroductionRelation to Previous WorkModelling the Blur GradientPlanar Orientation Estimation Algorithm◦Estimating Tilt◦Estimating Slant

Test Data and Experimental Results

IntroductionA focus-based method to recover the

orientation of a textured planar surface patch from a single image

Relation to Previous WorkDepth from DefocusShape from Texture◦Distance effect◦Foreshortening effect

Modelling the Blur Gradient(1/3)The goal of planar orientation algorithms

is to accurately estimate the slant and tilt of a 3D plane

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: sd

Modelling the Blur Gradient(3/3)

• camera’s aperture :F• focal length: f• sensor distance: • blur radius: • image position: (x,y)

sd

• is a linear function of inverse depth

• blur radius is a linear function of image position (x, y) • the blur gradient

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

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

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

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.)

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

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

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