eight light and image

Light as a ray Light is most frequently thought of as a set of rays Traveling from a light source To a viewer By way of some surface(s) that reflect it

Light as a ray Light is most frequently thought of as a set of rays Traveling from a light source To a viewer By way of some surface(s) that reflect it Often, it’s many surfaces

Pinhole camera object Placing Produces object a very small hole in very a dark box Produces a faint image on the opposite side of the box Technically, the image is upside-down image plane light ray hole object

Pinhole camera The hole constrains where the rays can project Farther objects must project closer to the center Nearer objects, toward the sides

Pinhole camera The hole constrains where the rays can project Farther objects produce smaller images Nearer objects, larger images

Perspective projection object Image plane A camera projects a 3D world down to a 2D world The particular type of projection is called perspective projection We can describe perspective projection in terms of coordinates light ray Y f y Z Y = height of object Z = depth y = “height” of projection (note image is really upside down) f = focal length y/f = Y/Z y = fY/Z

Perspective projection (X, Y, Z) Image plane A camera projects a 3D world down to a 2D world The particular type of projection is called perspective projection We can describe perspective projection in terms of coordinates light ray Y f (x,y) Z x = fX/Z y = fY/Z (x,y) = (fX/Z, fY/Z)

Perspective projection (X, Y, Z) Image plane Decreasing the focal length makes the image smaller But also increases your field of view Lenses with short focal lengths are therefore called wide-angle lenses light ray Y f (x,y) Z x = fX/Z y = fY/Z (x,y) = (fX/Z, fY/Z)

Perspective projection (X, Y, Z) Image plane Increasing the focal length makes the image bigger But decreases your field of view Lenses with large focal lengths are called telephoto lenses light ray Y f Z (x,y) x = fX/Z y = fY/Z (x,y) = (fX/Z, fY/Z)

Light as a ray Light is most frequently thought of as a set of rays Traveling from a light source To a viewer By way of some surface(s) that reflect it

Lambertian reflection Surface reflection Surface reflectance is very complicated There are two main models of reflectance Specular (glossy) surfaces bounce it directly off Lambertian (matte) bounce it evenly in all directions incident ray reflected rays specular reflection (highlights) incident ray reflected rays Lambertian reflection (matte/diffuse)

Specular reflection Mirror-like reflection Mirrors are near-perfect specular reflectors Incident and reflected rays have at (almost) the same angle In practice, there’s some scattering All wavelengths are (usually) reflected equally So reflection has the color of the light incident ray reflected rays

Lambertian reflection Lambertian/diffuse/matte reflection Perfect non-glossy paint Light reflected equally in all directions Brightness depends on illumination angle When light hits and an angle, it’s spread out over a wider area (1/sin θ times wider) So the intensity of the light coming out is dimmed by sin θ Not all wavelengths are reflected equally The reflection has the color of the surface (at least if the light is white) θ d θ d/sin θ beam spreads out by 1/sin θ

Surface normals θ (For reasons that will be clearer later) We usually measure the angle a little differently We use the angle between the light and A line sticking straight out from the surface This is called the surface’s normal This means the dimming factor is cos θ Because we measured θ differently surface normal θ d θ d/cos θ beam spreads out by 1/cos θ

Specular and diffuse reflection

Shape from shading Perceptual system computes surface curvature from intensity gradients Bias to assume light source is above the head

Modeling Pictorial techniques to bring out object shape Chiaroscuro very important Point-lights generate strong shadows Highlights Carvaggio, Incredulity of St. Thomas

Modeling

Modeling with lighting Key light Offset from camera Mood, modeling Fill light Fills in rest of scene Keeps shadows under control Others Back light, rim light, …

Rim lighting key fill rim John Lasseter, Toy Story (USA, 1995) key fill rim Used to emphasize outline of an object in shadow Key light leaves left edge of character in shadow Can’t make out object boundaries Spooky (Tom Hanks isn’t supposed to be spooky) Weak rim light brings up contrast at object boundary Tom Hanks safely de-spooked

The Boris Karloff effect

The Locket (USA, 1947)

Cohen bros., Blood Simple (USA, 1984)

The French Connection (1971)

Dark City (1998)

Dark city

Dark City

Dark City

Dark City

Subsurface scattering Translucent materials don’t reflect light directly It bounces around inside the material for a while and comes out in a different location This is important for modeling skin and wax

Components of reflection and transmission                       specular diffuse SSS combined

Problems with pinhole cameras object Because the aperture (hole) is so small, pinhole cameras let very little light in This means you need to use very bright lights or very long exposures to capture images on film image plane light ray small aperture object

Problems with pinhole cameras object We can make the aperture larger But then it doesn’t constraint where the rays go We lose focus Light from objects spreads out Images of objects overlap image plane light rays big aperture object

Thin lens projection A lens allows many rays to focus to the same point Brighter image But only focuses a single depth plane Image plane lens light rays aperture

Depth of field

Thin lens projection That’s partly why cameras with lenses still have an aperture By shrinking the aperture We get closer to a pinhole camera And we get wider depth of field Image plane lens light rays aperture

Aperture and depth of field

Deep focus

Citizen Kane (Welles, 1941)

Citizen Kane

Shallow focus Rules of the Game, (Renoir, 1939)

magnetic field electric field time Light as a wave Light is an oscillation between electric and magnetic fields Frequency/wavelength determines apparent color But color is perceptual property, not a physical one Amplitude determines apparent brightness High frequency Short wavelength Low frequency Long wavelength

Oscillation stretch time speed Occurs when two forces are in opposition Causes energy to alternate between two forms Guitar string Motion stretches the string Which slows the motion And eventually reverses it But then the stretch reverses And so on … Commonly takes the form of a sine wave speed(t) = cos ωt stretch(t) = sin ωt ω is the frequency of the oscillation (how often it repeats)

Waves Waves are oscillations that move through space Frequency Rate of cycling Period (how far between cycles) Amplitude (intensity): Size of the oscillation w(x) = A sin(ωx)

Chromatic aberration A lens actually focuses different wavelengths (colors) at slightly different depths In extreme cases, this leads to a colored blur around bright lights blue/violet artifacts

The human eye Lens and iris Photoreceptors Retinal processing Rods (b/w) Cones (color) Fovea Small (size of thumbnail at 3’) High resolution Color vision Macula, and periphery Low resolution, wide FOV Retinal processing Gain control Edge enhancement? Simple motion detection lens/iris rods cones retinal ganglion

Chromatic aberration in the eye blue is poorly focused on the retina green is well focused on the retina The blue photoreceptors of the eye evolved first So the have lower resolution And nature didn’t try to fix the chromatic aberration of the eye So blue light is significantly out of focus on the retina Blue backgrounds in PowerPoint are evil

Photoreceptors Rods Cones Colors seem to fade in low light Found mostly in the macula and periphery Very sensitive to light But don’t detect color Cones Found in the fovea Less sensitive Color sensitive Colors seem to fade in low light

Trichromacy Having different cones for every possible wavelength would be bad We just have three kinds of cones “Blue” cones: short wavelengths “Green” cones: intermediate wavelengths “Red” cones: long wavelengths However, their responses overlap The eye reduces all the wavelengths at a given pixel to just the total “amount” of “red”, “green”, and “blue”

Components of a color image