Implications In any collocated camera+projector setup, there is a special illumination pattern that appears undistorted to the camera, for arbitrary scene geometry. The pattern may or may not be periodic !! Existing structured light scanners can now be used to super- resolve in addition to recovering depth information ( with suitable modifications ) Preliminary Experimental Results on surpassing the diffraction limit for crossed optical axes Prasanna Rangarajan Indranil Sinharoy Vikrant R Bhakta

Picture of Experimental Setup Top View Side View Special thanks to Indranil for the pictures Camera Projector Angle between optical axes of camera and projector is ≈ 30 degrees The projector center-of-perspective is designed to be in the XZ plane of the camera coordinate system, which is centered at the camera center-of-perspective  horizontally collocated setup Projector Optical Axis Camera Optical AxisBaseline

Picture of Experimental Setup Top View Side View Camera Projector The target is parallel to the camera image plane during calibration In all other cases, the target is parallel to the projector. Consequently, the camera perceives the calibration target as being tilted, and having depth variation Special thanks to Indranil for the pictures

Details of Camera, Projector Setup

More details…

EXPERIMENT - 1 USAF target positioned in front of calibration target such that it is parallel to the projector image plane Illuminate scene with pre-warped vertical pattern of spatial frequency 90 cycles/mm in camera image plane Pre-warped illumination pattern 1400 x 1050 ( appears aliased due to MATLAB display issues ) Zoomed-in view of pre-warped illumination pattern 201x 201 patch Notice the perspective warp in illumination pattern

super-resolving a planar USAF target that is oriented at an angle of 30 degrees w.r.t camera Notice the perspective distortion in the image of the USAF target camera optical cutoff ≈ 180 lp/mm in the image plane size of image is 601 x 601

super-resolving a planar USAF target that is oriented at an angle of 30 degrees w.r.t camera Notice the periodic pattern super-imposed on the USAF target. Although the target appears to experience perspective distortion, the pattern appears un-distorted to the camera ( evident in the Fourier domain ) carrier frequency ≈ 90 lp/mm in the camera image plane

super-resolving a planar USAF target that is oriented at an angle of 30 degrees w.r.t camera Notice that modulation is able to resolve vertical edges in the oriented USAF target NOTE: The carrier pattern might appear slightly aliased due to MATLAB’s display issues The fringe patterns on the target appear oriented due to the tilt in the target

super-resolving a planar USAF target that is oriented at an angle of 30 degrees w.r.t camera Notice the peak in the fourier spectrum of the cosine/sine modulated image of the scene, at ≈ 90 lp/mm in the camera image plane

super-resolving a planar USAF target that is oriented at an angle of 30 degrees w.r.t camera Notice the peak in the fourier spectrum of the complex sinusoidal modulated image of the scene, at ≈ 90 lp/mm in the camera image plane

super-resolving a planar USAF target that is oriented at an angle of 30 degrees w.r.t camera Notice that modulation in the vertical direction is able to extend the bandwidth of the imaging system in the vertical direction

super-resolving a planar USAF target that is oriented at an angle of 30 degrees w.r.t camera size of raw image is 601 x 601

super-resolving a planar USAF target that is oriented at an angle of 30 degrees w.r.t camera size of super resolved image is 841 x 841 Notice enhanced resolution in vertical elements of group -1 ( zoom-in for better view ) There is a faint artifact that is regular and appears to be perspectively distorted

EXPERIMENT - 2 Barcode target positioned in front of calibration target such that it is parallel to the projector image plane Illuminate scene with pre-warped vertical pattern of spatial frequency 90 cycles/mm in camera image plane Pre-warped illumination pattern 1400 x 1050 ( appears aliased due to MATLAB display issues ) Zoomed-in view of pre-warped illumination pattern 201x 201 patch Notice the perspective warp in illumination pattern

super-resolving a planar barcode target that is oriented at an angle of 30 degrees w.r.t camera Notice the perspective distortion in the image of the barcode target camera optical cutoff ≈ 180 lp/mm in the image plane size of image is 601 x 601 the fine spatial in the barcodes is missing ( zoom-in for better view )

super-resolving a planar USAF target that is oriented at an angle of 30 degrees w.r.t camera Notice the periodic pattern super-imposed on the USAF target. Although the target appears to experience perspective distortion, the pattern appears un-distorted to the camera ( evident in the Fourier domain ) carrier frequency ≈ 90 lp/mm in the camera image plane

super-resolving a planar USAF target that is oriented at an angle of 30 degrees w.r.t camera Notice that modulation is able to resolve vertical edges in the 1D & 2D barcodes NOTE: The carrier pattern might appear slightly aliased due to MATLAB’s display issues The fringe patterns in the barcodes appear oriented due to the tilt in the target

super-resolving a planar barcode target that is oriented at an angle of 30 degrees w.r.t camera Notice the peak in the fourier spectrum of the cosine/sine modulated image of the scene, at ≈ 90 lp/mm in the camera image plane

super-resolving a planar barcode target that is oriented at an angle of 30 degrees w.r.t camera Notice the peak in the fourier spectrum of the complex sinusoidal modulated image of the scene, at ≈ 90 lp/mm in the camera image plane

super-resolving a planar barcode target that is oriented at an angle of 30 degrees w.r.t camera Notice that modulation in the vertical direction is able to extend the bandwidth of the imaging system in the vertical direction

super-resolving a planar barcode target that is oriented at an angle of 30 degrees w.r.t camera size of raw image is 601 x 601

super-resolving a planar barcode target that is oriented at an angle of 30 degrees w.r.t camera size of super resolved image is 841 x 841 Notice enhanced resolution in the vertical barcode & the 2D bar code The vertical barcode is fully resolved There is a faint artifact that is regular and appears to be perspectively distorted