CSE559A Lecture 6

Continue on Light, eye/camera, and color

BRDF (Bidirectional Reflectance Distribution Function)

Diffuse Reflection

• Dull, matte surface like chalk or latex paint

• Most often used in computer vision

• Brightness does depend on direction of illumination

Diffuse reflection governed by Lambert’s law: $I_d = k_d N\cdot L I_i$

• $N$: surface normal
• $L$: light direction
• $I_i$: incident light intensity
• $k_d$: albedo

Photometric Stereo

Suppose there are three light sources, $L_1, L_2, L_3$, and we have the following measurements:

We can solve for $N$ by taking the dot product of $N$ and each light direction and then solving the system of equations.

Will not do this in the lecture.

Specular Reflection

• Mirror-like surface

• $V$: view direction
• $R$: reflection direction
• $\theta_i$: angle between the incident light and the surface normal

Near-perfect mirror have a high light around $R$.

common model:

• $k_s$: specular reflection coefficient
• $n_s$: shininess (imperfection of the surface)
• $I_i$: incident light intensity

Phong illumination model

• Phong approximation of surface reflectance
  • Assume reflectance is modeled by three compoents
    • Diffuse reflection
    • Specular reflection
    • Ambient reflection

• $k_a$: ambient reflection coefficient
• $I_a$: ambient light intensity
• $k_d$: diffuse reflection coefficient
• $k_s$: specular reflection coefficient
• $n_s$: shininess
• $I_i$: incident light intensity

Many other models.

Measuring BRDF

Use Gonioreflectometer.

• Device for measuring the reflectance of a surface as a function of the incident and reflected angles.
• Can be used to measure the BRDF of a surface.

BRDF dataset:

• MERL dataset
• CURET dataset

Camera/Eye

DSLR Camera

• Pinhole camera model
• Lens
• Aperture (the pinhole)
• Sensor
• …

Digital Camera block diagram

Scanning protocols:

• Global shutter: all pixels are exposed at the same time
• Interlaced: odd and even lines are exposed at different times
• Rolling shutter: each line is exposed as it is read out

Eye

• Pupil
• Iris
• Retina
• Rods and cones
• …

Eye Movements

• Saccade
  • Can be consciously controlled. Related to perceptual attention.
  • 200ms to initiation, 20 to 200ms to carry out. Large amplitude.
• Smooth pursuit
  • Tracking an object
  • Difficult w/o an object to track!
• Microsaccade and Ocular microtremor (OMT)
  • Involuntary. Smaller amplitude. Especially evident during prolonged fixation.

Contrast Sensitivity

• Uniform contrast image content, with increasing frequency
• Why not uniform across the top?
• Low frequencies: harder to see because of slower intensity changes
• Higher frequencies: harder to see because of ability of our visual system to resolve fine features

Color Perception

Visible light spectrum: 380 to 780 nm

• 400 to 500 nm: blue
• 500 to 600 nm: green
• 600 to 700 nm: red

HSV model

We use Gaussian functions to model the sensitivity of the human eye to different wavelengths.

• Hue: color (the wavelength of the highest peak of the sensitivity curve)
• Saturation: color purity (the variance of the sensitivity curve)
• Value: color brightness (the highest peak of the sensitivity curve)

Color Sensing in Camera (RGB)

• 3-chip vs. 1-chip: quality vs. cost

Bayer filter:

• Why more green?
  • Human eye is more sensitive to green light.

Color spaces

Images in python:

As matrix.

import matplotlib.pyplot as plt
 
from mpl_toolkits.mplot3d import Axes3D
from skimage import io
 
def plot_rgb_3d(image_path):
    image = io.imread(image_path)
    r, g, b = image[:,:,0], image[:,:,1], image[:,:,2]
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    ax.scatter(r.flatten(), g.flatten(), b.flatten(), c=image.reshape(-1, 3)/255.0, marker='.')
    ax.set_xlabel('Red')
    ax.set_ylabel('Green')
    ax.set_zlabel('Blue')
    plt.show()
 
plot_rgb_3d('image.jpg')

Other color spaces:

• YCbCr (fast to compute, usually used in TV)
• HSV
• L*a*b* (CIELAB, perceptually uniform color space)

Most information is in the intensity channel.