Image Formation & Camera FundamentalsRODNEY DOCKTER

APRIL 3 2019

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Outline• Physics Review

• A Brief History Of Capturing Images

• How are images formulated?

• Camera Models: Lenses, Depth of Field, Field of View

• Human Eye

• Digital Image Representation

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Electromagnetic Spectrum

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Electromagnetic Spectrum

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• Radio Waves – Wireless Communication

• Microwaves – Ramen Noodles

• Infrared – Heat Waves

• Visible Light – What your eyes see

• Ultraviolet – Sunburn, curing silicone, invisible patterns

• X-Rays – Penetrates Tissue

•Gamma Rays – Most Energetic

Visible Spectrum

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Visible light extends in wavelength from ~400 to ~700 nanometers

Quantum Theory of Light

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• Isaac Newton, 1704 - Light is a stream of particles traveling in a straight line. Each particle is called a quantum and each quantum of light is a photon. The intensity of light is measured by the number of photons.

• Refraction occurs when light enters a different medium causing the velocity of light to change. This change then bends the direction of the light.

• When white light enters a prism the light is split into the full spectrum. Shorter wavelengths (violet) are refracted at a greater angle than longer wavelengths (red).

How do we capture an image?

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Image Formation• Two parts to the image formation process:

• (1) The Geometry, which determines where in the image the plane the projection of a point in the scene will be located.

• (2) The Physics of Light, which determines the brightness of a point in the image plane.

• Simple model: f(x,y) = i(x,y) r(x,y)

• i: illumination, r: reflectance

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Image Formation• Design of a basic camera, Version 1:• Put a piece of film in front of an object

• Coat film with light sensitive material (Changes depending on light intensity)

• Do we get a reasonable image? Probably not… Blurring

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Image Formation• Design of a basic camera, Version 2:• View through a hole: Reduces blurring

• The opening is known as aperture.

• How does this transform the image? (It flips it)

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Image Formation• Camera Obscura (4th Century BC China -> 16th century Leonardo da Vinci)

• Limitations:

• Aperture too big: blurry image

•Aperture to small: Requires long exposure time

•Aperture much to small: diffraction through pinhole + blurry image.

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Image Formation• Adding a lens

• Lens based Camera Obscura, 1568

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Image Formation• 1826 – The first photograph – Joseph Nicéphore Niépce

• Camera Obscura focused onto a pewter plate coated with asphalt. ~8 hour exposure.

• Basic mathematical model – Pinhole Camera

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Image Formation• Conventional Camera Design

• Early film based cameras, 1960’s

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Image Formation

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Animal Eye:Early AnatomicalStudies

Camera Obscura +Pinhole camera model4th-15th centuries

First PhotographicCamera. Niépce1820’s

Image Formation

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Camera Models

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Camera Models• Pinhole Camera Model

• The simplest method to form an image of a 3D scene on a 2D surface

• Rays of light pass through a “pinhole” and form an inverted images of the object on the image plane

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http://web.anagram.at

Perspective Projection:

𝑥 =𝑓 𝑋

𝑍𝑦 =

𝑓 𝑌

𝑍

𝑃 𝑋, 𝑌, 𝑍 → 𝑝(𝑥, 𝑦)

f: focal length, distance between pinhole and image plane

Camera Models

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• Is an image being formed on the screen?

• Yes, but not a clear one

𝒓′

𝑓′=𝒓

𝑧

𝑥′

𝑓′=𝑥

𝑧

𝑦′

𝑓′=𝑦

𝑧(𝑟′≠ 𝑓′)

Camera Models

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• What is the effect of aperture size?

• Large aperture: light from the sourcespreads across the image (i.e. not properly focused) making it blurry

• Small aperture: reduces blurring butit limits the amount of light enteringthe camera and causes light diffraction

Camera Models

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• Shrinking the aperture

•Why not make the aperture as small as possible?• Less light gets through

Camera Models

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• Shrinking the aperture more

• What happens if we keep decreasing aperture size?

• When light passes through a small hole, it does not travel in a straight line and is scattered in many directions (diffraction)

Camera Models

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• Pinhole too big – many directionsare averaged, blurring the image

• Pinhole too small – diffractioneffects blur the image

• Generally, pinhole cameras aredark because a very small amountof rays from a point in the scene reach the image plane

Camera Models

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• Problems with pinholes

• Pinhole size (aperture) must be SMALL to obtain a clear image

• However as pinhole size gets smaller, LESSlight is received by the image plane

• If pinhole is comparable to wavelength ofincoming light, DIFFRACTION effects blur the image

• OPTIMAL pinhole size is obtained when:

pinhole diameter: 𝑑 = 2 𝑓′λ

Example: 𝑓′ = 50𝑚𝑚, λ = 600𝑛𝑚 (𝑟𝑒𝑑)𝑑 = 0.36𝑚𝑚

Lenses

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• The reason for lenses:

• Gather more light from each point in the scenePinhole

Lens

Lenses

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• Upgrading from a pinhole to a lens.

• Lens redirect light rays emanating from the object

• Lenses improve image quality, leading to sharper images

Lenses

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• A lens focuses parallel rays onto a single focal point• Focal point at a distance ‘f’ beyond the plane of the lens

• ‘f’ is a function of the shape and index of the refraction of the lens

• Aperture of diameter ‘D’ restricts the range of the rays• Aperture may be on either side of the lens

• Lenses are typically spherical (Easier to produce)

Focal Point

Optical Center

Lenses

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• Properties of “thin” lenses (ideal lenses)

• Light rays passing through the center are not deviated

• Light rays passing through a point far away from the center are deviated more

Lenses

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• Properties of “thin” lenses (ideal lenses)

• All parallel rays converge to single point

• Rays passing perpendicular to the lens pass through the Focal Point

Lenses

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• Properties of “thin” lenses (ideal lenses)

• The plane parallel to the lens at the focal point is the called the Focal Plane

• The distance between the lens and the focal plane is the Focal Length (f)

Lenses

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• Thin lens equation:

• Any object satisfying this equation is in focus

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𝑑𝑂+

1

𝑑𝑖=1

𝑓

Lenses

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• Lets verify the thin lens equation

• Assume an object at distance u from the lens plane

Lenses

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• Using similar triangles:

Lenses

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• Using similar triangles:

Lenses

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• Combining these equations:

Lenses

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• The thin lens assumption assumes the lens has no thickness (this is not physically possible)

• When our lens does have thickness, the shape of the image plane becomes slightly concave

• By adding more elements to lens, we can correct for this and the focus region can be made roughly planar

Optical Axis

Aperture

D

f

Lenses

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• Lens Aperture (f/Number)

• Lenses have the ability to control the amount of light that reaches the camera sensor.

• The f/number (𝑛𝑓) is the ratio of the focal length of the lens to the diameter of the aperture (𝐷 = 2𝑟)

• Lens Power (P): Reciprocal of focal length

𝑛𝑓 =𝑓

2𝑟

P =1

𝑓

Depth of Field

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• A lens focuses light onto the film

• There is a specific distance at which objects are “in focus”

• Other points project to a “circle of confusion in the image

• Lens shape affects this distance

Depth of Field

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• The size of the blur circle is proportional to aperture size

Depth of Field

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• Changing the aperture size affects depth of field

• A smaller aperture increases the range in which an object is approximately in focus

• Small aperture also reduces the amount of light – increased exposure needed to compensate

Depth of Field

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• Changing the aperture of a camera also changes the amount of the image that is in focus

• This amount (or range of depths) is called the depth of field

Depth of Field

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• Changing the aperture size affects depth of field

• Smaller aperture increases the range in which an object is approximately in focus (but we need to increase exposure time)

• A larger aperture decreases the depth of field (but lower exposure time required

Depth of Field

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• Smaller aperture increases the range in which an object is approximately in focus

Depth of Field

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• The range of depths over which the scene is approximately sharp (i.e. in focus)

Depth of Field

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Large aperture,Small depth of field

Small aperture,Large depth of field

Depth of Field

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• Small Apetures(e.g. f11, f16, f22) only let a smallamount of light through

• Large Apertures(e.g. f4, f5.6, f8) let through a lot of light

• For use a sunny day, you mightneed to use a small aperture toget correct exposure

Field of View (Zoom)

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• The cone of viewing directions of the camera

• Inversely proportional to focal length

Field of view is governed by the size of the camera retina:

𝜑 = 𝑡𝑎𝑛−1𝑑

2𝑓

Field of View (Zoom)

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• Increasing focallength

• Decreased fieldof view…

Lens Flaws

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• Chromatic Aberration

• Lens has different refractive indices for different wavelengths

• Can cause fringing: lens cannot focus all the colors from a single point

Lens Flaws

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• Chromatic Aberration example:

Lens Flaws

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• Radial Distortion

• Straight lines becomes distorted as we move further away from the center of the image

• Deviations are most noticeable for rays that pass through the edge of the lens

Lens Flaws

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• Radial Distortion example

No Distortion Pin Cushion Barrel

Lens Flaws

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• Tangential Distortion

• Lens is not exactly parallel to the imaging plane

• Image plane becomes skewed

The Human Eye

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• Cameras are a copy of the human eye

The Human Eye

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• We intentionally made cameras that act similar to the human eye

• … Because that’s what we understand

The Human Eye

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• The primary difference is what captures the light

The Human Eye

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• The other major difference is that the human eyes perceive depth very well

• Human vision system transforms light stimuli on the retina into a mental construct of a stable 3D world

• Our 3D perception of the world is invariant to a wide range of changes in illumination, size, shape, and brightness of the scene

• The best 3D cameras in the world do not come close to human 3D perception

Digital Image Formation

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Digital Image(Grayscale)

Digital Image Formation• First digitally scanned photograph

• 1957, 176x176 pixels

• Origins of digital cameras come fromdigital scanners

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Digital Image Formation• A digital camera replaces film with a sensor array

• Each cell in the array contains a light-sensitive diode that converts photons to electrons

• Two common varieties:

• Charge coupled Device (CCD)

• Complementary Metal OxideSemiconductor (CMOS)

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Digital Image Formation

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8 Bits/Pixel

0

128

255

Digital Image Formation• When a continuous scene is imaged on the array (grid) formed by a CMOS, the continuous image is divided into discrete elements

• The picture elements (pixels) that are captured represented a spatially sampled version of the image

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Digital Image Formation• Our spatially sampled image can then be represented by numbers according to the brightness of each pixel

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Digital Image Formation

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Original Image Region of Interest Matrix Representation(R,G,B)

Digital Image Formation

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Digital Image Formation• Digital Camera Properties

• Focus – Shifts the depth that is in focus

• Focal Length – Adjusts the zoom (wide angle or telephoto)

• Aperture – Adjusts the depth of field and amount of light let into sensor

• Exposure Time – How long an image is exposed. More exposure = more light, more blur

• ISO – Adjusts the sensitivity of the image sensor. Basically a gain function for digital cameras to increase brightness.

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Digital Image Formation• Camera Exposure

• ISO Number• Sensitivity of the film or the sensor

• Can go as high as 1600 or 3200

• Shutter Speed• How fast the shutter is opened and closed

• f/stop• The size of the aperture

• 1.0 ~ 32

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Digital Image Formation• Exposure:

• Defined as the total amount of light falling on the film

• Exposure = Illuminance * Time

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Digital Image Formation• Exposure is controlled by the shutter. When closed the film is not exposed to light.

• Exposure time is simply the time interval between opening and closing the shutter

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Digital Image Formation• Long Exposure

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Digital Image Formation• Short Exposure

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Digital Image Formation• Varying Exposure Levels

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Image File Formats• Many image file formats adhere to the simple model shown below (line by line, no breaks)

• The header contains at least the width and height of the image

• Most headers begin with a signature or “magic number” (a short sequence of bytes for identifying the file format)

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Image File Formats• GIF (Graphics Interchange Format)

• PNG (Portable Network Graphics)

• JPEG (Joint Photographic Experts Group)

• TIFF (Tagged Image File Format)

• PGM (Portable Gray Map)

• FITS (Flexible Image Transport System)

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Image File Formats• PBM/PGM/PPM Format

• A very basic image format for greyscale images (Not really used anymore)

• Closely-related formats:• PBM (Portable Bitmap) for binary images (1 bit/pixel)

• PPM (Portable Pixelmap) for color images (24 bits/pixel)

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Image File Formats• JPEG Format

• Comparatively complex image format (very common)

• Format consists of a sequence of markers or marker segments

• Each marker indicates the start of a marker segment that contains data bytes according to:• Marker: FF xx s1 s2 [data bytes]

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