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Shadow Removal Using Illumination Invariant Image

Shadow Removal Using Illumination Invariant Image. Graham D. Finlayson, Steven D. Hordley, Mark S. Drew. Presented by: Eli Arbel. Outline. Introduction Removing Shadows Reconstruction Illumination Invariant Images Summary. Introduction. Why shadow removal ? Computer Vision

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Shadow Removal Using Illumination Invariant Image

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  1. Shadow Removal Using Illumination Invariant Image Graham D. Finlayson, Steven D. Hordley, Mark S. Drew Presented by: Eli Arbel

  2. Outline • Introduction • Removing Shadows • Reconstruction • Illumination Invariant Images • Summary Shadow Removal Seminar

  3. Introduction • Why shadow removal ? • Computer Vision • Image Enhancement • Illumination Re-rendering Shadow Removal Seminar

  4. Introduction, cont’d Shadow Removal Seminar

  5. Introduction, cont’d • What is shadow ? Region lit by skylight only Region lit by sunlight and skylight A shadow is a local change in illumination intensity and (often) illumination color. Shadow Removal Seminar

  6. Introduction, cont’d • Assumptions for shadow removal: • Only Hard shadows can be removed • No overlapping of object and shadow boundaries • Planckian light source • Narrow band sensors of the capturing device Shadow Removal Seminar

  7. Outline • Introduction • Removing Shadows • Reconstruction • Illumination Invariant Images • Summary Shadow Removal Seminar

  8. Method For Removing Shadows • An RGB image is input • Shadow identification is based on edge detection Shadow Removal Seminar

  9. Yes, under some assumptions… Discriminating Edges • Can we factor out illumination changes (intensity and color) ? • More on that later… Shadow Removal Seminar

  10. Illumination Invariant Image RGB Channels Illumination Invariant Image Edge Map Channels Edge Maps Discriminating Edges, cont’d Input Image Shadow Removal Seminar

  11. Discriminating Edges - Formally • Let us denote one of the three channel edge maps as (x,y) • And denote the invariant image edge map as gs(x,y) • we apply a Thresholding operator on each of the channel edge maps as follows: Where ||(x,y)|| and ||gs(x,y)|| are the gradient magnitudes of channel edge map and illumination invariant edge map respectively Shadow Removal Seminar

  12. Illumination Invariant Image RGB Channels Illumination Invariant Image Edge Map Discriminating Edges, cont’d Input Image Channels Edge Maps Thresholded edge maps Shadow Removal Seminar

  13. Outline • Introduction • Removing Shadows • Reconstruction • Illumination Invariant Images • Summary Shadow Removal Seminar

  14. Reconstructing the Image • For each channel, we now have an edge map in which shadow edges are removed: • T–Thresholding operator • – Derivative operator in x direction • – Derivative operator in y direction Shadow Removal Seminar

  15. Re-integrating Edge Information • We would like to integrate • So first, we calculate the Laplacian out of the gradient: Shadow Removal Seminar

  16. Re-integrating Edge Information – cont’d • Now we solve by applying the Inverse Laplacian: This is a private case of the Wiess reconstruction process where we have only two filters, and . Shadow Removal Seminar

  17. More on Reconstruction • The re-integration step recover uniquely up to a multiplicative (additive) constant – DC. • A heuristic approach is used to find this constant. For each shadow-free channel image: • Consider the top 1-percentile pixels • Compute their average • Map this value to white Shadow Removal Seminar

  18. Some results Shadow Removal Seminar

  19. Some results – cont’d Shadow Removal Seminar

  20. Some results – cont’d Shadow Removal Seminar

  21. Some results – cont’d Shadow Removal Seminar

  22. Outline • Introduction • Removing Shadows • Reconstruction • Illumination Invariant Images • Summary Shadow Removal Seminar

  23. Illumination Invariant Image – Theoretical Analysis • Sensor response at any pixel can be formulated as: R= Reflectance L = Illumination S = Sensor Sensitivity Shadow Removal Seminar

  24. Assumption 1: Capturing Device Sensors • Sensor response is narrow band, i.e. a Dirac Function: Shadow Removal Seminar

  25. Assumption 1: Capturing Device Sensors – cont’d Shadow Removal Seminar

  26. Assumption 2: Planckian Light Source Scene illumination is assumed to be Planckian, i.e. it falls very near to the Planckian locus: Shadow Removal Seminar

  27. Assumption 2: Planckian Light Source – cont’d Planck's law of black body radiation:The spectral intensity of electromagnetic radiation from a black body at temperature T asa function of wavelength: Shadow Removal Seminar

  28. Assumption 2: Planckian Light Source – cont’d Planck’s Law is a good approximation for incandescent and daylight illuminants CIE D55 2500k 5500k Shadow Removal Seminar

  29. Assumption 2: Planckian Light Source – cont’d • To model varying illumination power, we add an intensity constant I: • In addition, it can be shown that , thus: Shadow Removal Seminar

  30. Assumption 2: Planckian Light Source – cont’d Shadow Removal Seminar

  31. Towards Color Constancy at a Pixel Depends on illuminant intensity Depends on Surface reflectance Depends on Illuminant color Shadow Removal Seminar

  32. Towards Color Constancy at a Pixel – cont’d Simplifying notations: Shadow Removal Seminar

  33. Towards Color Constancy at a Pixel –Dropping the Intensity term Shadow Removal Seminar

  34. Color Constancy at a Pixel The relations: Can be written in matrix notation: Shadow Removal Seminar

  35. Color Constancy at a Pixel – cont’d We just solved the one-dimensional color constancy problem at a pixel ! Reminder: - Camera sensor response Shadow Removal Seminar

  36. Color Constancy at a Pixel Examples Log-Chromaticity Differences for seven surfaces under 10 Planckian illuminants Shadow Removal Seminar

  37. Color Constancy at a Pixel Examples – cont’d Log-Chromaticity Differences for the Macbeth Color Checker with HP912 Digital Still Camera Shadow Removal Seminar

  38. Color Constancy at a Pixel Examples – cont’d Log-Chromaticity Differences for the Macbeth Color Checker with Nikon D-100 Shadow Removal Seminar

  39. Illumination Invariant Images - Examples Shadow Removal Seminar

  40. Outline • Introduction • Removing Shadows • Reconstruction • Illumination Invariant Images • Summary Shadow Removal Seminar

  41. Summary • A method for shadow removal in single image using 1-D illumination invariant image presented • Shadow-free edge-maps are re-integrated using Wiess reconstruction method • 1-D Illumination invariant image is obtained relying on physical properties of lightness and camera sensors Shadow Removal Seminar

  42. References • G. D. Finlayson, S.D. Hordley and M.S. Drew. Removing Shadows From Images • G. D. Finlayson, S. D. Hordley and M. S. Drew. Removing shadows from images. Presentation for ECCV02, 2002. • Grahm. D. Finlayson, Steven. D. Hordley. Color Constancy at a Pixel. • Model-Based Object Tracking in Road Traffic Scenes, Dieter Koller • ואבישי אדלראורי בריט. הסרת צל מסדרת תמונות ומתמונה בודדת Shadow Removal Seminar

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