3D Computer Vision. Photometric stereo. Prof. Didier Stricker

Size: px
Start display at page:

Download "3D Computer Vision. Photometric stereo. Prof. Didier Stricker"

Transcription

1 3D Computer Vision Photometric stereo Prof. Didier Stricker Kaiserlautern University DFKI Deutsches Forschungszentrum für Künstliche Intelligenz 1

2 Physical parameters of image forma2on Op2cal Sensor s lens type focal length, field of view, aperture Geometric Type of projec2on Camera calibra2on Two/Mul2- views geometry Photometric (radiometry) Type, direc2on, intensity of light reaching sensor Surfaces reflectance proper2es Inference from shading

3 Image forma2on What determines the brightness of an image pixel? Light source proper.es Surface shape and orienta.on Sensor characteris.cs Exposure Op.cs Surface reflectance proper.es Slide by L. Fei- Fei

4 Radiance and irradiance Radiance (L) energy exiting a source or surface Irradiance (E) incoming energy E L E E L L E L Which (E or L) does a camera sensor array directly measure?

5 Radiometry Radiometry is the part of image forma.on concerned with the rela.on among the amounts of q q q light energy emi@ed from light sources, reflected from surfaces, and registered by sensors. 5

6 Foreshortening A big source, viewed at a glancing angle, must produce the same effect as a small source viewed frontally. This phenomenon is known as foreshortening. 6

7 Solid Angle Solid angle is defined by the projected area of a surface patch onto a unit sphere of a point. (Solid angle is subtended by a point and a surface patch.) * da projected onto surface of the sphere of radius r: da cos(theta) * Ra.o of surface areas of spheres of radii 1 and r: 4 pi / (4 pi r^2) = 1/r^2 7

8 Solid Angle Arc length r dφ dφ r 8

9 Solid Angle Solid angle is defined by the projected area of a surface patch onto a unit sphere of a point. da = rdθ r sin θ dφ = r 2 sin θ dθ dφ da 2π TotalArea = π φ θ r 2 sin θ dθ dφ = 4π r 2 =0 =0 da dw = 2 = sin θ dθ dφ r 9

10 Solid Angle Similarly, solid angle due to a line segment is θ dl dφ r 10

11 Radiance The distribu.on of light in space is a func.on of posi.on and direc.on. The appropriate unit for measuring the distribu.on of light in space is radiance, which is defined as the power (the amount of energy per unit.me) traveling at some point in a specified direc.on, per unit area perpendicular to the direc7on of travel, per unit solid angle. In short, radiance is the amount of light radiated from a point (into a unit solid angle, from a unit area). Radiance = Power / (solid angle x foreshortened area) W/sr/m2 W is Wa@, sr is steradian, m2 is meter- squared 11

12 Radiance Radiance from ds to dr Radiance = Power / (solid angle x foreshortened area) 12

13 Radiance Example: Infinitesimal source and surface patches Radiance = Power / (solid angle x foreshortened area) Power or radiant flux emi@ed of the source Radiance leaving x1 in the direc.on of x2 Illuminated surface dψ r 2 dψ L(x1,x1 x 2 ) = = dw2 cosθ1da1 da2 cosθ 2 cosθ1da1 dw2 = Source da2 cosθ 2 r2 13

14 Radiance Radiance = Power / (solid angle x foreshortened area) Power at x1 leaving to x2 Illuminated surface dψ = L(x1,x1 x 2 )dw2 cosθ1da1 = Source L(x1,x1 x 2 )da2 cosθ 2 cosθ1da1 r2 dw2 = da2 cosθ 2 r2 14

15 Radiance Illuminated surface Source Let the radiance arriving at x2 from the direc.on of x1 is dψ r 2 dψ L(x 2,x1 x 2 ) = = dw1 cosθ 2 da2 da1 cosθ1 cosθ 2 da2 dw1 = da1 cosθ1 r2 15

16 Radiance The medium is vacuum, that is, it does not absorb energy. Therefore, the power reaching point x2 is equal to the power leaving for x2 from x1. Radiance is constant along a straight line. Illuminated surface L(x1, x1 x2 ) = L(x2, x1 x2 ) Source 16

17 Radiance If the medium is vacuum, power is preserved. 17

18 Point Source Many light sources are physically small compared with the environment in which they stand. Such a light source is approximated as an extremely small sphere, in fact, a point. Such a light source is known as a point source. 18

19 Radiance Intensity If the source is a point source, we use radiance intensity. Radiance intensity = Power / (solid angle) Illuminated surface dψ r 2 dψ I= = dw da2 cosθ 2 dw = da2 cosθ 2 r2 Source 19

20 Light at Surfaces When light strikes a surface, it may be absorbed, transmi@ed, or sca@ered; usually, combina.on of these effects occur. It is common to assume that all effects are local and can be explained with a local interac2on model. In this model: q q q The radiance leaving a point on a surface is due only to radiance arriving at this point. Surfaces do not generate light internally and treat sources separately. Light leaving a surface at a given wavelength is due to light arriving at that wavelength. 20

21 Light at Surfaces In the local interac.on model, fluorescence, [absorb light at one wavelength and then radiate light at a different wavelength], and emission [e.g., warm surfaces emits light in the visible range] are neglected. 21

22 Irradiance (E) Irradiance is the total incident power per unit area. Irradiance = Power / Area 22

23 Irradiance What is the irradiance due to source from angle? 23

24 Irradiance What is the irradiance due to source from angle? da Irradiance = dψ Li ( x,θ i, φi )dw cos θ i da = = Li ( x,θ i, φi )dw cos θ i da da radiance foreshortening factor Solid angle 24

25 Irradiance What is the total irradiance? Integrate over the whole hemisphere. E= 2π 0 π 2 0 L cosθ sin θ dθ dφ solid angle Since dω = sin θ dθ dφ 25

26 Irradiance Exercise: Calculate the irradiance at O due to a plate source at O. 26

27 Irradiance due to a Point Source For a point source, Radiance intensity = Power / (solid angle) dψ r 2 dψ I= = dw dai cosθ i dw = da cosθ dψ = I i 2 i r dai cosθ i r2 cosθ i dψ Irradiance = =I 2 dai r 27

28 The Relationship Between Image Intensity and Object We assume that there is no power loss Diameter of Radiance in the lens. lens The power to the lens is dψ = Lobject da0 cos α dw0 Radiance of object 28

29 Area of the lens The Relationship Between with diameter d Image Intensity and Object The solid angle for the en.re lens is Diameter of Radiance lens dw0 πd ( = 2 / 4 ) cosθ r2 The power emi@ed to the lens is dψ = Lobject da0 cos α dw0 π d 2 cosθ = Lobject da0 cos α 4r 2 29

30 The Relationship Between Image Intensity and Object Diameter of The solid angle at O can be wri@en in Radiance lens two ways. da0 cos α dap cos θ = 2 r2 OA ' Note that OA ' = f / cosθ Therefore 3 da0 cos α dap cos θ = 2 r f2 30

31 The Relationship Between Image Intensity and Object Diameter of Combine Radiance lens 3 da0 cos α dap cos θ = 2 r f2 dψ = Lobject da0 cos α π d 2 cosθ 4r 2 to get 2 d π dψ = Lobject cos 4 θ dap 4 f 31

32 The Relationship Between Image Intensity and Object Diameter of Therefore the irradiance on the image Radiance lens plane is 2!d $ dψ! π $ Irradiance = = # & Lobject # & cos 4 θ dap " 4 % "f% The irradiance is converted to pixel intensi.es, which is directly propor.onal to the radiance of the object. 32

33 Image irradiance on the image plane The image irradiance (E) is proportional to the object radiance (L) Lens diameter Angle off op.cal axis ' π! d $2 * E = ) # & cos 4 θ, L )( 4 " f %,+ Focus distance What the image reports to us via pixel values What we really want to know

34 Fundamental radiometric rela2on ' π! d $2 * E = ) # & cos 4 θ, L )( 4 " f %,+ S. B. Kang and R. Weiss, Can we calibrate a camera using an image of a flat, textureless Lamber.an surface? ECCV 2000.

35 Surface Characteristics We want to describe the rela.onship between incoming light and reflected light. This is a func.on of both the direc.on in which light arrives at a surface and the direc.on in which it leaves. 35

36 Bidirectional Reflectance Distribution Function (BRDF) BRDF is defined as the ra.o of the radiance in the outgoing direc.on to the incident irradiance. 36

37 Bidirectional Reflectance Distribution Function (BRDF) The radiance leaving a surface due to irradiance in a par7cular direc7on is easily obtained from the defini.on of BRDF: 37

38 Bidirectional Reflectance Distribution Function (BRDF) The radiance leaving a surface due to irradiance in all incoming direc7ons is where Omega is the incoming hemisphere. 38

39 BRDFs can be incredibly complicated

40 Lambertian Surface A Lamber7an surface has constant BRDF. A Lamber.an surface looks equally bright from any view direc.on. The image intensi.es of the surface only changes with the illumina.on direc.ons. constant 40

41 Lambertian Surface For a Lamber.an surface, the outgoing radiance is propor.onal to the incident radiance. constant If the light source is a point source, a pixel intensity will only be a func.on of Remember, for a point source cosθ i dψ Irradiance = =I 2 dai r BRDF is constant, we speak about Albedo Albedo: frac.on of incident irradiance reflected by the surface 41

42 Specular Surface The glossy or mirror like surfaces are called specular surfaces. Radia.on arriving along a par.cular direc.on can only leave along the specular direc.on, obtained from the surface normal. *The term Specular comes from the La.n word speculum, meaning mirror. 42

43 Specular Surface Few surfaces are ideally specular. Specular surfaces commonly reflect light into a lobe of direc.ons around the specular direc.on. 43

44 Lambertian + Specular Model Rela.vely few surfaces are either ideal diffuse or perfectly specular. The BRDF of many surfaces can be approximated as a combina.on of a Lamber.an component and a specular component. 44

45 Lamber2an + Specular Model Lamber.an Lamber.an + Specular 45

46 Radiosity Radiosity, defined as the total power leaving a point. To obtain the radiosity of a surface at a point, we can sum the radiance leaving the surface at that point over the whole hemisphere. 46

47 Part II Shading

48 Point Source For a point source, Radiance intensity = Power / (solid angle) dψ r 2 dψ I= = dw dai cosθ i dw = da cosθ dψ = I i 2 i r dai cosθ i r2 cosθ i dψ Irradiance = =I 2 dai r 48

49 A Point Source at Infinity The radiosity due to a point source at infinity is S( x) N( x) x B: radiosity (total power leaving the surface per unit area) ρ: albedo (frac.on of incident irradiance reflected by the surface) N: unit normal S: source vector (magnitude propor.onal to intensity of the source) 49

50 Local Shading Models for Point Sources The radiosity due to light generated by a set of point sources is Radiosity due to source s 50

51 Local Shading Models for Point Sources If all the sources are point sources at infinity, then 51

52 Ambient Illumination For some environments, the total irradiance a patch obtains from other patches is roughly constant and roughly uniformly distributed across the input hemisphere. In such an environment, it is possible to model the effect of other patches by adding an ambient illumina7on term to each patch s radiosity. + B0 52

53 Photometric Stereo If we are given a set of images of the same scene taken under different given ligh.ng sources, can we recover the 3D shape of the scene? 53

54 Photometric Stereo For a point source and a Lamber.an surface, we can write the image intensity as Suppose we are given the intensi.es under three ligh.ng condi.ons: Camera and object are fixed, so a par.cular pixel intensity is only a func.on of ligh.ng direc.on si. 54

55 Photometric Stereo Stack the pixel intensi.es to get a vector The surface normal can be found as Since n is a unit vector As a result, we can find the surface normal of each point, hence the 3D shape 55

56 More than Three Light Sources Get better results by using more lights T ' I1 $ ' s 1 $ %! " = %! " ρn % " % " %& I N "# %&stn "# Least squares solu.on: ~ I = Sn ~ ST I = ST Sn 1 T T ~ n= S S S I N 1 = (N 3)(3 1) ( ) Solve for ρ, n as before pseudo inverse

57 Photometric Stereo When the source direc.ons are not given, they can be es.mated from three known surface normals. 57

58 Photometric Stereo 58

59 Photometric Stereo Surface normals 3D shape 59

60 Photometric Stereo (by Xiaochun Cao) 60

61 Results Estimate light source directions Compute surface normals Compute albedo values Estimate depth from surface normals Relight the object (with original texture and uniform albedo)

62 Computer vision applica2on Finding the direc.on of light source P. Nillius and J.- O. Eklundh, Automa.c es.ma.on of the projected light source direc.on, CVPR 2001

63 Computer vision applica2on Detec.ng composite photos: Fake photo Real photo M. K. Johnson and H. Farid, Exposing Digital Forgeries by Detec.ng Inconsistencies in Ligh.ng, ACM Mul.media and Security Workshop, 2005.

64 Applica2on: Detec2ng composite photos Fake photo Real photo

65 Thank you!

Capturing light. Source: A. Efros

Capturing light. Source: A. Efros Capturing light Source: A. Efros Review Pinhole projection models What are vanishing points and vanishing lines? What is orthographic projection? How can we approximate orthographic projection? Lenses

More information

Understanding Variability

Understanding Variability Understanding Variability Why so different? Light and Optics Pinhole camera model Perspective projection Thin lens model Fundamental equation Distortion: spherical & chromatic aberration, radial distortion

More information

Lecture 22: Basic Image Formation CAP 5415

Lecture 22: Basic Image Formation CAP 5415 Lecture 22: Basic Image Formation CAP 5415 Today We've talked about the geometry of scenes and how that affects the image We haven't talked about light yet Today, we will talk about image formation and

More information

INFOGR Computer Graphics. J. Bikker - April-July Lecture 10: Shading Models. Welcome!

INFOGR Computer Graphics. J. Bikker - April-July Lecture 10: Shading Models. Welcome! INFOGR Computer Graphics J. Bikker - April-July 2016 - Lecture 10: Shading Models Welcome! Today s Agenda: Introduction Light Transport Materials Sensors Shading INFOGR Lecture 10 Shading Models 3 Introduction

More information

Image Formation: Light and Shading. Introduction to Computer Vision CSE 152 Lecture 3

Image Formation: Light and Shading. Introduction to Computer Vision CSE 152 Lecture 3 Image Formation: Light and Shading CSE 152 Lecture 3 Announcements Homework 1 is due Apr 11, 11:59 PM Homework 2 will be assigned on Apr 11 Reading: Chapter 2: Light and Shading Geometric image formation

More information

Announcements. Image Formation: Light and Shading. Photometric image formation. Geometric image formation

Announcements. Image Formation: Light and Shading. Photometric image formation. Geometric image formation Announcements Image Formation: Light and Shading Homework 0 is due Oct 5, 11:59 PM Homework 1 will be assigned on Oct 5 Reading: Chapters 2: Light and Shading CSE 252A Lecture 3 Geometric image formation

More information

Announcements. Radiometry and Sources, Shadows, and Shading

Announcements. Radiometry and Sources, Shadows, and Shading Announcements Radiometry and Sources, Shadows, and Shading CSE 252A Lecture 6 Instructor office hours This week only: Thursday, 3:45 PM-4:45 PM Tuesdays 6:30 PM-7:30 PM Library (for now) Homework 1 is

More information

Overview. Radiometry and Photometry. Foundations of Computer Graphics (Spring 2012)

Overview. Radiometry and Photometry. Foundations of Computer Graphics (Spring 2012) Foundations of Computer Graphics (Spring 2012) CS 184, Lecture 21: Radiometry http://inst.eecs.berkeley.edu/~cs184 Overview Lighting and shading key in computer graphics HW 2 etc. ad-hoc shading models,

More information

Measuring Light: Radiometry and Cameras

Measuring Light: Radiometry and Cameras Lecture 11: Measuring Light: Radiometry and Cameras Computer Graphics CMU 15-462/15-662, Fall 2015 Slides credit: a majority of these slides were created by Matt Pharr and Pat Hanrahan Simulating a pinhole

More information

Paths, diffuse interreflections, caching and radiometry. D.A. Forsyth

Paths, diffuse interreflections, caching and radiometry. D.A. Forsyth Paths, diffuse interreflections, caching and radiometry D.A. Forsyth How we got here We want to render diffuse interreflections strategy: compute approximation B-hat, then gather B = E +(ρk)e +(ρk)( ˆB

More information

Radiometry. Radiometry. Measuring Angle. Solid Angle. Radiance

Radiometry. Radiometry. Measuring Angle. Solid Angle. Radiance Radiometry Radiometry Computer Vision I CSE5A ecture 5-Part II Read Chapter 4 of Ponce & Forsyth Solid Angle Irradiance Radiance BRDF ambertian/phong BRDF Measuring Angle Solid Angle By analogy with angle

More information

Announcement. Lighting and Photometric Stereo. Computer Vision I. Surface Reflectance Models. Lambertian (Diffuse) Surface.

Announcement. Lighting and Photometric Stereo. Computer Vision I. Surface Reflectance Models. Lambertian (Diffuse) Surface. Lighting and Photometric Stereo CSE252A Lecture 7 Announcement Read Chapter 2 of Forsyth & Ponce Might find section 12.1.3 of Forsyth & Ponce useful. HW Problem Emitted radiance in direction f r for incident

More information

CENG 477 Introduction to Computer Graphics. Ray Tracing: Shading

CENG 477 Introduction to Computer Graphics. Ray Tracing: Shading CENG 477 Introduction to Computer Graphics Ray Tracing: Shading Last Week Until now we learned: How to create the primary rays from the given camera and image plane parameters How to intersect these rays

More information

Radiometry and reflectance

Radiometry and reflectance Radiometry and reflectance http://graphics.cs.cmu.edu/courses/15-463 15-463, 15-663, 15-862 Computational Photography Fall 2018, Lecture 16 Course announcements Homework 4 is still ongoing - Any questions?

More information

Radiometry. Reflectance & Lighting. Solid Angle. Radiance. Radiance Power is energy per unit time

Radiometry. Reflectance & Lighting. Solid Angle. Radiance. Radiance Power is energy per unit time Radiometry Reflectance & Lighting Computer Vision I CSE5A Lecture 6 Read Chapter 4 of Ponce & Forsyth Homework 1 Assigned Outline Solid Angle Irradiance Radiance BRDF Lambertian/Phong BRDF By analogy with

More information

Photometric Stereo.

Photometric Stereo. Photometric Stereo Photometric Stereo v.s.. Structure from Shading [1] Photometric stereo is a technique in computer vision for estimating the surface normals of objects by observing that object under

More information

CS-184: Computer Graphics. Today. Lecture 22: Radiometry! James O Brien University of California, Berkeley! V2014-S

CS-184: Computer Graphics. Today. Lecture 22: Radiometry! James O Brien University of California, Berkeley! V2014-S CS-184: Computer Graphics Lecture 22: Radiometry James O Brien University of California, Berkeley V2014-S-15-1.0 Today Radiometry: measuring light Local Illumination and Raytracing were discussed in an

More information

Reflectance & Lighting

Reflectance & Lighting Reflectance & Lighting Computer Vision I CSE5A Lecture 6 Last lecture in a nutshell Need for lenses (blur from pinhole) Thin lens equation Distortion and aberrations Vignetting CS5A, Winter 007 Computer

More information

Introduction to Computer Vision. Introduction CMPSCI 591A/691A CMPSCI 570/670. Image Formation

Introduction to Computer Vision. Introduction CMPSCI 591A/691A CMPSCI 570/670. Image Formation Introduction CMPSCI 591A/691A CMPSCI 570/670 Image Formation Lecture Outline Light and Optics Pinhole camera model Perspective projection Thin lens model Fundamental equation Distortion: spherical & chromatic

More information

Photometric Stereo. Lighting and Photometric Stereo. Computer Vision I. Last lecture in a nutshell BRDF. CSE252A Lecture 7

Photometric Stereo. Lighting and Photometric Stereo. Computer Vision I. Last lecture in a nutshell BRDF. CSE252A Lecture 7 Lighting and Photometric Stereo Photometric Stereo HW will be on web later today CSE5A Lecture 7 Radiometry of thin lenses δa Last lecture in a nutshell δa δa'cosα δacos β δω = = ( z' / cosα ) ( z / cosα

More information

2/1/10. Outline. The Radiance Equation. Light: Flux Equilibrium. Light: Radiant Power. Light: Equation. Radiance. Jan Kautz

2/1/10. Outline. The Radiance Equation. Light: Flux Equilibrium. Light: Radiant Power. Light: Equation. Radiance. Jan Kautz Outline Jan Kautz Basic terms in radiometry Radiance Reflectance The operator form of the radiance equation Meaning of the operator form Approximations to the radiance equation 2005 Mel Slater, 2006 Céline

More information

dq dt I = Irradiance or Light Intensity is Flux Φ per area A (W/m 2 ) Φ =

dq dt I = Irradiance or Light Intensity is Flux Φ per area A (W/m 2 ) Φ = Radiometry (From Intro to Optics, Pedrotti -4) Radiometry is measurement of Emag radiation (light) Consider a small spherical source Total energy radiating from the body over some time is Q total Radiant

More information

CS184 LECTURE RADIOMETRY. Kevin Wu November 10, Material HEAVILY adapted from James O'Brien, Brandon Wang, Fu-Chung Huang, and Aayush Dawra

CS184 LECTURE RADIOMETRY. Kevin Wu November 10, Material HEAVILY adapted from James O'Brien, Brandon Wang, Fu-Chung Huang, and Aayush Dawra CS184 LECTURE RADIOMETRY Kevin Wu November 10, 2014 Material HEAVILY adapted from James O'Brien, Brandon Wang, Fu-Chung Huang, and Aayush Dawra ADMINISTRATIVE STUFF Project! TODAY Radiometry (Abridged):

More information

Radiance. Radiance properties. Radiance properties. Computer Graphics (Fall 2008)

Radiance. Radiance properties. Radiance properties. Computer Graphics (Fall 2008) Computer Graphics (Fall 2008) COMS 4160, Lecture 19: Illumination and Shading 2 http://www.cs.columbia.edu/~cs4160 Radiance Power per unit projected area perpendicular to the ray per unit solid angle in

More information

dq dt I = Irradiance or Light Intensity is Flux Φ per area A (W/m 2 ) Φ =

dq dt I = Irradiance or Light Intensity is Flux Φ per area A (W/m 2 ) Φ = Radiometry (From Intro to Optics, Pedrotti -4) Radiometry is measurement of Emag radiation (light) Consider a small spherical source Total energy radiating from the body over some time is Q total Radiant

More information

A question from Piazza

A question from Piazza Radiometry, Reflectance, Lights CSE 252A Lecture 6 A question from Piazza 1 Announcements HW1 posted HWO graded, will be returned today If anyone has any registration issues, talk to me. Appearance: lighting,

More information

And if that 120MP Camera was cool

And if that 120MP Camera was cool Reflectance, Lights and on to photometric stereo CSE 252A Lecture 7 And if that 120MP Camera was cool Large Synoptic Survey Telescope 3.2Gigapixel camera 189 CCD s, each with 16 megapixels Pixels are 10µm

More information

The Rendering Equation. Computer Graphics CMU /15-662

The Rendering Equation. Computer Graphics CMU /15-662 The Rendering Equation Computer Graphics CMU 15-462/15-662 Review: What is radiance? Radiance at point p in direction N is radiant energy ( #hits ) per unit time, per solid angle, per unit area perpendicular

More information

Starting this chapter

Starting this chapter Computer Vision 5. Source, Shadow, Shading Department of Computer Engineering Jin-Ho Choi 05, April, 2012. 1/40 Starting this chapter The basic radiometric properties of various light sources Develop models

More information

The Light Field. Last lecture: Radiometry and photometry

The Light Field. Last lecture: Radiometry and photometry The Light Field Last lecture: Radiometry and photometry This lecture: Light field = radiance function on rays Conservation of radiance Measurement equation Throughput and counting rays Irradiance calculations

More information

CS201 Computer Vision Lect 4 - Image Formation

CS201 Computer Vision Lect 4 - Image Formation CS201 Computer Vision Lect 4 - Image Formation John Magee 9 September, 2014 Slides courtesy of Diane H. Theriault Question of the Day: Why is Computer Vision hard? Something to think about from our view

More information

Assignment #2. (Due date: 11/6/2012)

Assignment #2. (Due date: 11/6/2012) Computer Vision I CSE 252a, Fall 2012 David Kriegman Assignment #2 (Due date: 11/6/2012) Name: Student ID: Email: Problem 1 [1 pts] Calculate the number of steradians contained in a spherical wedge with

More information

Measuring Light: Radiometry and Photometry

Measuring Light: Radiometry and Photometry Lecture 10: Measuring Light: Radiometry and Photometry Computer Graphics and Imaging UC Berkeley CS184/284A, Spring 2016 Radiometry Measurement system and units for illumination Measure the spatial properties

More information

Global Illumination The Game of Light Transport. Jian Huang

Global Illumination The Game of Light Transport. Jian Huang Global Illumination The Game of Light Transport Jian Huang Looking Back Ray-tracing and radiosity both computes global illumination Is there a more general methodology? It s a game of light transport.

More information

Lights, Surfaces, and Cameras. Light sources emit photons Surfaces reflect & absorb photons Cameras measure photons

Lights, Surfaces, and Cameras. Light sources emit photons Surfaces reflect & absorb photons Cameras measure photons Reflectance 1 Lights, Surfaces, and Cameras Light sources emit photons Surfaces reflect & absorb photons Cameras measure photons 2 Light at Surfaces Many effects when light strikes a surface -- could be:

More information

Global Illumination. CMPT 361 Introduction to Computer Graphics Torsten Möller. Machiraju/Zhang/Möller

Global Illumination. CMPT 361 Introduction to Computer Graphics Torsten Möller. Machiraju/Zhang/Möller Global Illumination CMPT 361 Introduction to Computer Graphics Torsten Möller Reading Foley, van Dam (better): Chapter 16.7-13 Angel: Chapter 5.11, 11.1-11.5 2 Limitation of local illumination A concrete

More information

Radiometry & BRDFs CS295, Spring 2017 Shuang Zhao

Radiometry & BRDFs CS295, Spring 2017 Shuang Zhao Radiometry & BRDFs CS295, Spring 2017 Shuang Zhao Computer Science Department University of California, Irvine CS295, Spring 2017 Shuang Zhao 1 Today s Lecture Radiometry Physics of light BRDFs How materials

More information

Reflection models and radiometry Advanced Graphics

Reflection models and radiometry Advanced Graphics Reflection models and radiometry Advanced Graphics Rafał Mantiuk Computer Laboratory, University of Cambridge Applications To render realistic looking materials Applications also in computer vision, optical

More information

Electromagnetic waves and power spectrum. Rays. Rays. CS348B Lecture 4 Pat Hanrahan, Spring 2002

Electromagnetic waves and power spectrum. Rays. Rays. CS348B Lecture 4 Pat Hanrahan, Spring 2002 Page 1 The Light Field Electromagnetic waves and power spectrum 1 10 10 4 10 6 10 8 10 10 10 1 10 14 10 16 10 18 10 0 10 10 4 10 6 Power Heat Radio Ultra- X-Rays Gamma Cosmic Infra- Red Violet Rays Rays

More information

Radiometry. Computer Graphics CMU /15-662, Fall 2015

Radiometry. Computer Graphics CMU /15-662, Fall 2015 Radiometry Computer Graphics CMU 15-462/15-662, Fall 2015 Last time we discussed light & color Image credit: Licensed under CC BY-SA 3.0 via Commons https://commons.wikimedia.org/wiki/file:em_spectrum.svg#/media/file:em_spectrum.svg

More information

Lecture 7 - Path Tracing

Lecture 7 - Path Tracing INFOMAGR Advanced Graphics Jacco Bikker - November 2016 - February 2017 Lecture 7 - I x, x = g(x, x ) ε x, x + S ρ x, x, x I x, x dx Welcome! Today s Agenda: Introduction Advanced Graphics 3 Introduction

More information

CS6670: Computer Vision

CS6670: Computer Vision CS6670: Computer Vision Noah Snavely Lecture 20: Light, reflectance and photometric stereo Light by Ted Adelson Readings Szeliski, 2.2, 2.3.2 Light by Ted Adelson Readings Szeliski, 2.2, 2.3.2 Properties

More information

Ligh%ng and Reflectance

Ligh%ng and Reflectance Ligh%ng and Reflectance 2 3 4 Ligh%ng Ligh%ng can have a big effect on how an object looks. Modeling the effect of ligh%ng can be used for: Recogni%on par%cularly face recogni%on Shape reconstruc%on Mo%on

More information

Introduction to Computer Vision. Week 8, Fall 2010 Instructor: Prof. Ko Nishino

Introduction to Computer Vision. Week 8, Fall 2010 Instructor: Prof. Ko Nishino Introduction to Computer Vision Week 8, Fall 2010 Instructor: Prof. Ko Nishino Midterm Project 2 without radial distortion correction with radial distortion correction Light Light Light! How do you recover

More information

CS667 Lecture Notes: Radiometry

CS667 Lecture Notes: Radiometry CS667 Lecture Notes: Radiometry Steve Marschner Cornell University 23-28 August 2007 Radiometry is a system for describing the flow of radiant energy through space. It is essentially a geometric topic

More information

Ligh%ng in OpenGL. The Phong Illumina%on Model. Vector Background

Ligh%ng in OpenGL. The Phong Illumina%on Model. Vector Background Ligh%ng in OpenGL The Phong Illumina%on Model Vector Background 1 Vector Dot Product The dot product of two vectors is a number:! x $ # 1 v 1 = # y 1 # " z 1 %! x $ # 2 v 2 = # y 2 # " z 2 % In GLSL you

More information

Measuring Light: Radiometry and Photometry

Measuring Light: Radiometry and Photometry Lecture 14: Measuring Light: Radiometry and Photometry Computer Graphics and Imaging UC Berkeley Radiometry Measurement system and units for illumination Measure the spatial properties of light New terms:

More information

EE Light & Image Formation

EE Light & Image Formation EE 576 - Light & Electric Electronic Engineering Bogazici University January 29, 2018 EE 576 - Light & EE 576 - Light & The image of a three-dimensional object depends on: 1. Shape 2. Reflectance properties

More information

The Rendering Equation. Computer Graphics CMU /15-662, Fall 2016

The Rendering Equation. Computer Graphics CMU /15-662, Fall 2016 The Rendering Equation Computer Graphics CMU 15-462/15-662, Fall 2016 Review: What is radiance? Radiance at point p in direction N is radiant energy ( #hits ) per unit time, per solid angle, per unit area

More information

Light Field = Radiance(Ray)

Light Field = Radiance(Ray) Page 1 The Light Field Light field = radiance function on rays Surface and field radiance Conservation of radiance Measurement Irradiance from area sources Measuring rays Form factors and throughput Conservation

More information

Illumination in Computer Graphics

Illumination in Computer Graphics Illumination in Computer Graphics Ann McNamara Illumination in Computer Graphics Definition of light sources. Analysis of interaction between light and objects in a scene. Rendering images that are faithful

More information

Image Processing 1 (IP1) Bildverarbeitung 1

Image Processing 1 (IP1) Bildverarbeitung 1 MIN-Fakultät Fachbereich Informatik Arbeitsbereich SAV/BV (KOGS) Image Processing 1 (IP1) Bildverarbeitung 1 Lecture 20: Shape from Shading Winter Semester 2015/16 Slides: Prof. Bernd Neumann Slightly

More information

Radiometry Measuring Light

Radiometry Measuring Light 1 Radiometry Measuring Light CS 554 Computer Vision Pinar Duygulu Bilkent University 2 How do we see? [Plato] from our eyes flows a light similar to the light of the sun [Chalcidius, middle ages] Therefore,

More information

Cameras and Radiometry. Last lecture in a nutshell. Conversion Euclidean -> Homogenous -> Euclidean. Affine Camera Model. Simplified Camera Models

Cameras and Radiometry. Last lecture in a nutshell. Conversion Euclidean -> Homogenous -> Euclidean. Affine Camera Model. Simplified Camera Models Cameras and Radiometry Last lecture in a nutshell CSE 252A Lecture 5 Conversion Euclidean -> Homogenous -> Euclidean In 2-D Euclidean -> Homogenous: (x, y) -> k (x,y,1) Homogenous -> Euclidean: (x, y,

More information

CS5670: Computer Vision

CS5670: Computer Vision CS5670: Computer Vision Noah Snavely Light & Perception Announcements Quiz on Tuesday Project 3 code due Monday, April 17, by 11:59pm artifact due Wednesday, April 19, by 11:59pm Can we determine shape

More information

Philpot & Philipson: Remote Sensing Fundamentals Interactions 3.1 W.D. Philpot, Cornell University, Fall 12

Philpot & Philipson: Remote Sensing Fundamentals Interactions 3.1 W.D. Philpot, Cornell University, Fall 12 Philpot & Philipson: Remote Sensing Fundamentals Interactions 3.1 W.D. Philpot, Cornell University, Fall 1 3. EM INTERACTIONS WITH MATERIALS In order for an object to be sensed, the object must reflect,

More information

CMSC427 Shading Intro. Credit: slides from Dr. Zwicker

CMSC427 Shading Intro. Credit: slides from Dr. Zwicker CMSC427 Shading Intro Credit: slides from Dr. Zwicker 2 Today Shading Introduction Radiometry & BRDFs Local shading models Light sources Shading strategies Shading Compute interaction of light with surfaces

More information

Other approaches to obtaining 3D structure

Other approaches to obtaining 3D structure Other approaches to obtaining 3D structure Active stereo with structured light Project structured light patterns onto the object simplifies the correspondence problem Allows us to use only one camera camera

More information

Spectral Color and Radiometry

Spectral Color and Radiometry Spectral Color and Radiometry Louis Feng April 13, 2004 April 13, 2004 Realistic Image Synthesis (Spring 2004) 1 Topics Spectral Color Light and Color Spectrum Spectral Power Distribution Spectral Color

More information

Introduction to Radiosity

Introduction to Radiosity Introduction to Radiosity Produce photorealistic pictures using global illumination Mathematical basis from the theory of heat transfer Enables color bleeding Provides view independent representation Unfortunately,

More information

CS667 Lecture Notes: Radiometry

CS667 Lecture Notes: Radiometry CS667 Lecture Notes: Radiometry Steve Marschner Cornell University 3 6 September 2009 Radiometry is a system for describing the flow of radiant energy through space. It is essentially a geometric topic

More information

OPPA European Social Fund Prague & EU: We invest in your future.

OPPA European Social Fund Prague & EU: We invest in your future. OPPA European Social Fund Prague & EU: We invest in your future. Image formation and its physical basis Václav Hlaváč Czech Technical University in Prague Faculty of Electrical Engineering, Department

More information

THE goal of rendering algorithms is to synthesize images of virtual scenes. Global illumination

THE goal of rendering algorithms is to synthesize images of virtual scenes. Global illumination 2 Fundamentals of Light Transport He who loves practice without theory is like the sailor who boards ship without a rudder and compass and never knows where he may cast. Leonardo Da Vinci, 1452 1519 THE

More information

Comp 410/510 Computer Graphics. Spring Shading

Comp 410/510 Computer Graphics. Spring Shading Comp 410/510 Computer Graphics Spring 2017 Shading Why we need shading Suppose we build a model of a sphere using many polygons and then color it using a fixed color. We get something like But we rather

More information

Announcements. Lighting. Camera s sensor. HW1 has been posted See links on web page for readings on color. Intro Computer Vision.

Announcements. Lighting. Camera s sensor. HW1 has been posted See links on web page for readings on color. Intro Computer Vision. Announcements HW1 has been posted See links on web page for readings on color. Introduction to Computer Vision CSE 152 Lecture 6 Deviations from the lens model Deviations from this ideal are aberrations

More information

Local Illumination. CMPT 361 Introduction to Computer Graphics Torsten Möller. Machiraju/Zhang/Möller

Local Illumination. CMPT 361 Introduction to Computer Graphics Torsten Möller. Machiraju/Zhang/Möller Local Illumination CMPT 361 Introduction to Computer Graphics Torsten Möller Graphics Pipeline Hardware Modelling Transform Visibility Illumination + Shading Perception, Interaction Color Texture/ Realism

More information

Lighting affects appearance

Lighting affects appearance Lighting affects appearance 1 Source emits photons Light And then some reach the eye/camera. Photons travel in a straight line When they hit an object they: bounce off in a new direction or are absorbed

More information

Radiance. Pixels measure radiance. This pixel Measures radiance along this ray

Radiance. Pixels measure radiance. This pixel Measures radiance along this ray Photometric stereo Radiance Pixels measure radiance This pixel Measures radiance along this ray Where do the rays come from? Rays from the light source reflect off a surface and reach camera Reflection:

More information

13 Distribution Ray Tracing

13 Distribution Ray Tracing 13 In (hereafter abbreviated as DRT ), our goal is to render a scene as accurately as possible. Whereas Basic Ray Tracing computed a very crude approximation to radiance at a point, in DRT we will attempt

More information

Sources, shadows and shading

Sources, shadows and shading Sources, shadows and shading But how bright (or what colour) are objects? One more definition: Exitance of a source is the internally generated power radiated per unit area on the radiating surface similar

More information

Announcements. Rotation. Camera Calibration

Announcements. Rotation. Camera Calibration Announcements HW1 has been posted See links on web page for reading Introduction to Computer Vision CSE 152 Lecture 5 Coordinate Changes: Rigid Transformations both translation and rotatoin Rotation About

More information

Realistic Camera Model

Realistic Camera Model Realistic Camera Model Shan-Yung Yang November 2, 2006 Shan-Yung Yang () Realistic Camera Model November 2, 2006 1 / 25 Outline Introduction Lens system Thick lens approximation Radiometry Sampling Assignment

More information

Mosaics, Plenoptic Function, and Light Field Rendering. Last Lecture

Mosaics, Plenoptic Function, and Light Field Rendering. Last Lecture Mosaics, Plenoptic Function, and Light Field Rendering Topics in Image-ased Modeling and Rendering CSE291 J00 Lecture 3 Last Lecture Camera Models Pinhole perspective Affine/Orthographic models Homogeneous

More information

Epipolar geometry contd.

Epipolar geometry contd. Epipolar geometry contd. Estimating F 8-point algorithm The fundamental matrix F is defined by x' T Fx = 0 for any pair of matches x and x in two images. Let x=(u,v,1) T and x =(u,v,1) T, each match gives

More information

CS 5625 Lec 2: Shading Models

CS 5625 Lec 2: Shading Models CS 5625 Lec 2: Shading Models Kavita Bala Spring 2013 Shading Models Chapter 7 Next few weeks Textures Graphics Pipeline Light Emission To compute images What are the light sources? Light Propagation Fog/Clear?

More information

Lighting and Materials

Lighting and Materials http://graphics.ucsd.edu/~henrik/images/global.html Lighting and Materials Introduction The goal of any graphics rendering app is to simulate light Trying to convince the viewer they are seeing the real

More information

6. Illumination, Lighting

6. Illumination, Lighting Jorg s Graphics Lecture Notes 6. Illumination, Lighting 1 6. Illumination, Lighting No ray tracing in OpenGL! ray tracing: direct paths COP interreflection: soft shadows, color bleeding. umbra, penumbra,

More information

Lecture 15: Shading-I. CITS3003 Graphics & Animation

Lecture 15: Shading-I. CITS3003 Graphics & Animation Lecture 15: Shading-I CITS3003 Graphics & Animation E. Angel and D. Shreiner: Interactive Computer Graphics 6E Addison-Wesley 2012 Objectives Learn that with appropriate shading so objects appear as threedimensional

More information

rendering equation computer graphics rendering equation 2009 fabio pellacini 1

rendering equation computer graphics rendering equation 2009 fabio pellacini 1 rendering equation computer graphics rendering equation 2009 fabio pellacini 1 physically-based rendering synthesis algorithms that compute images by simulation the physical behavior of light computer

More information

Range Sensors (time of flight) (1)

Range Sensors (time of flight) (1) Range Sensors (time of flight) (1) Large range distance measurement -> called range sensors Range information: key element for localization and environment modeling Ultrasonic sensors, infra-red sensors

More information

CS4670/5760: Computer Vision

CS4670/5760: Computer Vision CS4670/5760: Computer Vision Kavita Bala! Lecture 28: Photometric Stereo Thanks to ScoC Wehrwein Announcements PA 3 due at 1pm on Monday PA 4 out on Monday HW 2 out on weekend Next week: MVS, sfm Last

More information

Global Illumination. CSCI 420 Computer Graphics Lecture 18. BRDFs Raytracing and Radiosity Subsurface Scattering Photon Mapping [Ch

Global Illumination. CSCI 420 Computer Graphics Lecture 18. BRDFs Raytracing and Radiosity Subsurface Scattering Photon Mapping [Ch CSCI 420 Computer Graphics Lecture 18 Global Illumination Jernej Barbic University of Southern California BRDFs Raytracing and Radiosity Subsurface Scattering Photon Mapping [Ch. 13.4-13.5] 1 Global Illumination

More information

Local vs. Global Illumination & Radiosity

Local vs. Global Illumination & Radiosity Last Time? Local vs. Global Illumination & Radiosity Ray Casting & Ray-Object Intersection Recursive Ray Tracing Distributed Ray Tracing An early application of radiative heat transfer in stables. Reading

More information

E (sensor) is given by; Object Size

E (sensor) is given by; Object Size A P P L I C A T I O N N O T E S Practical Radiometry It is often necessary to estimate the response of a camera under given lighting conditions, or perhaps to estimate lighting requirements for a particular

More information

General Principles of 3D Image Analysis

General Principles of 3D Image Analysis General Principles of 3D Image Analysis high-level interpretations objects scene elements Extraction of 3D information from an image (sequence) is important for - vision in general (= scene reconstruction)

More information

Monte Carlo Ray Tracing. Computer Graphics CMU /15-662

Monte Carlo Ray Tracing. Computer Graphics CMU /15-662 Monte Carlo Ray Tracing Computer Graphics CMU 15-462/15-662 TODAY: Monte Carlo Ray Tracing How do we render a photorealistic image? Put together many of the ideas we ve studied: - color - materials - radiometry

More information

rendering equation computer graphics rendering equation 2009 fabio pellacini 1

rendering equation computer graphics rendering equation 2009 fabio pellacini 1 rendering equation computer graphics rendering equation 2009 fabio pellacini 1 phsicall-based rendering snthesis algorithms that compute images b simulation the phsical behavior of light computer graphics

More information

Shading. Why we need shading. Scattering. Shading. Objectives

Shading. Why we need shading. Scattering. Shading. Objectives Shading Why we need shading Objectives Learn to shade objects so their images appear three-dimensional Suppose we build a model of a sphere using many polygons and color it with glcolor. We get something

More information

Today. Global illumination. Shading. Interactive applications. Rendering pipeline. Computergrafik. Shading Introduction Local shading models

Today. Global illumination. Shading. Interactive applications. Rendering pipeline. Computergrafik. Shading Introduction Local shading models Computergrafik Matthias Zwicker Universität Bern Herbst 2009 Today Introduction Local shading models Light sources strategies Compute interaction of light with surfaces Requires simulation of physics Global

More information

Computer Graphics (CS 4731) Lecture 16: Lighting, Shading and Materials (Part 1)

Computer Graphics (CS 4731) Lecture 16: Lighting, Shading and Materials (Part 1) Computer Graphics (CS 4731) Lecture 16: Lighting, Shading and Materials (Part 1) Prof Emmanuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI) Why do we need Lighting & shading? Sphere

More information

Engineered Diffusers Intensity vs Irradiance

Engineered Diffusers Intensity vs Irradiance Engineered Diffusers Intensity vs Irradiance Engineered Diffusers are specified by their divergence angle and intensity profile. The divergence angle usually is given as the width of the intensity distribution

More information

Introduction to Physically-Based Illumination, Radiosity and Shadow Computations for Computer Graphics

Introduction to Physically-Based Illumination, Radiosity and Shadow Computations for Computer Graphics Introduction to Physically-Based Illumination, Radiosity and Shadow Computations for Computer Graphics Eugene Fiume Department of Computer Science University of Toronto 1 CSC2522 Lecture Notes January,

More information

A Brief Overview of. Global Illumination. Thomas Larsson, Afshin Ameri Mälardalen University

A Brief Overview of. Global Illumination. Thomas Larsson, Afshin Ameri Mälardalen University A Brief Overview of Global Illumination Thomas Larsson, Afshin Ameri Mälardalen University 1 What is Global illumination? Global illumination is a general name for realistic rendering algorithms Global

More information

A Survey of Light Source Detection Methods

A Survey of Light Source Detection Methods A Survey of Light Source Detection Methods Nathan Funk University of Alberta Mini-Project for CMPUT 603 November 30, 2003 Abstract This paper provides an overview of the most prominent techniques for light

More information

Global Illumination. Global Illumination. Direct Illumination vs. Global Illumination. Indirect Illumination. Soft Shadows.

Global Illumination. Global Illumination. Direct Illumination vs. Global Illumination. Indirect Illumination. Soft Shadows. CSCI 420 Computer Graphics Lecture 18 Global Illumination Jernej Barbic University of Southern California BRDFs Raytracing and Radiosity Subsurface Scattering Photon Mapping [Angel Ch. 11] 1 Global Illumination

More information

Computer Graphics (CS 543) Lecture 7b: Intro to lighting, Shading and Materials + Phong Lighting Model

Computer Graphics (CS 543) Lecture 7b: Intro to lighting, Shading and Materials + Phong Lighting Model Computer Graphics (CS 543) Lecture 7b: Intro to lighting, Shading and Materials + Phong Lighting Model Prof Emmanuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI) Why do we need Lighting

More information

COMPUTER GRAPHICS COURSE. LuxRender. Light Transport Foundations

COMPUTER GRAPHICS COURSE. LuxRender. Light Transport Foundations COMPUTER GRAPHICS COURSE LuxRender Light Transport Foundations Georgios Papaioannou - 2015 Light Transport Light is emitted at the light sources and scattered around a 3D environment in a practically infinite

More information

Representing the World

Representing the World Table of Contents Representing the World...1 Sensory Transducers...1 The Lateral Geniculate Nucleus (LGN)... 2 Areas V1 to V5 the Visual Cortex... 2 Computer Vision... 3 Intensity Images... 3 Image Focusing...

More information

Lighting. Figure 10.1

Lighting. Figure 10.1 We have learned to build three-dimensional graphical models and to display them. However, if you render one of our models, you might be disappointed to see images that look flat and thus fail to show the

More information

Radiometry (From Intro to Optics, Pedrotti 1-4) Radiometry is measurement of Emag radiation (light) Consider a small spherical source Assume a black

Radiometry (From Intro to Optics, Pedrotti 1-4) Radiometry is measurement of Emag radiation (light) Consider a small spherical source Assume a black Radiometry (From Intro to Optics, Pedrotti -4) Radiometry is measurement of Emag radiation (light) Consider a small spherical source Assume a black body type emitter: uniform emission Total energy radiating

More information