Image Processing Lecture 2

-Gaurav Gupta-Shobhit Niranjan

Today

Image Formation (More Details) Camera Models Perspective Geometry Color Models

Human Visual System (HVS): The Eye Image is formed on

retina Photoreceptors (rods

and cones) are stimulated and generate visual signal

Received and processed by brain (Cortex)

Pin Hole Camera Model

Light enters through small hole. Image plane is placed between focal point

and object (to have “non-inverted” projection)

Perspective Geometry

Mapping from R3->R2

Convention image coordinate (u,v), object coordinate (x,y,z)

u = (f/z)x ; v = (f/z)y

f = focal length (by geometry)

The linear version is ( S = scale factor)

Contd..

Concept of Vanishing Line, Point and Horizon is important for Reconstruction from 2D image to 3D information

Vanishing point : The point where parallel lines at particular direction meet .

Two sets of parallel lines in different directions will give two vanishing points.

Two vanishing points form a vanishing line for the collection of parallel planes defined by these two sets of parallel lines.

The Horizon

Vanishing Line for ground plane Anything below it will be below horizon and

above it will be above horizon Different heights of viewer ?? What would be

affect on the horizon?

Interpretation of Calibration matrix It gives you location of the vanishing point. The homogeneous coordinate (x,y,0) is the

ideal point or point at infinity in the direction of (x,y). (how??) (guess how to represent point at infinity in x direction), where will this appear in Image

Camera Calibration

Why? To find how the object coordinated are projected in image plane

Parameters: Intrinsic & Extrinsic Model

contd..

From the figure, hence, In other words, =>

In some cases focal lengths can be different in x and y direction fu , fv

f, uo,vo are intrinsic parameters

Extrinsic Parameters

In general, the three dimensional world coordinates of a point will not be specfied in a frame whose origin is at the centre of projection

So we can transform by a linear transformation ( Rotation and Scale)

Where T is 4x4 transformation matrix, R pure rotation (rigid body), t is the rigid body translation

Types of Image Transformation (or Deformation)

Color Models

Three independent quantities are used to describe any particular color. (HVS)

Achromatic light has no color - its only attribute is quantity or intensity. Greylevel is a measure of intensity.

On the other hand, brightness or luminance is determined by the perception of the color

Color depends primarily on the reflectance properties of an object.

contd…

The tristimulus theory of color perception seems to imply that any color can be obtained from a mix of the three primaries, red, green and blue

Color models provide a standard way to specify a particular color and specifies a 3D coordinate system or subspace

Any color that can be specified using a model will correspond to a single point within the subspace it defines

RGB Model

CMY Model

RGB model asks what is added to black to get a particular color, the CMY (cyan-magenta-yellow) model asks what is subtracted from white.

Appropriate to absorption of colors, used in printing devices and filters

HSI Model

The hue is determined by the dominant wavelength The saturation is determined by the excitation purity,

and depends on the amount of white light mixed with the hue

the intensity is determined by the actual amount of light

YIQ

YIQ (luminance-inphase-quadrature) is Recoding of RGB for color television

Some points to think about..

what is the best way to apply the image processing techniques color images ?

Which color space to choose ? If we want to increase the contrast in a dark

image by histogram equalization, can we just equalize each color independently?

Some quick facts

Normally Image is array of RGB values of pixels in BGR order

N-bit , m channel Image => It has m color spaces having N bit quantized data per color space per pixel (Ex. 8 bit RGB Image)

Very Simple data structure is Bitmap Format and Raw

JPEG widely used to store/capture images but it is compressed form

Home Work

Install OpenCV (Intel Open Source Lib) http://sourceforge.net/projects/opencvlibrary Check its documentation and see how image

is described by IplImage data structurehttp://www.cs.bham.ac.uk/resources/courses/robotics/doc/opencvdocs/

Try to write and run sample programs given

in OpenCV tutorial and see for different images loss in JPEG format I will mail you.

ThE eNd