Imaging geometry

Imaging Geometry
Mithun kumar kar
Department of Electrical Engineering
BALASORE COLLEGE OF ENGINEERING AND TECHNOLOGY, BALASORE
August 12, 2020
Mithun kumar kar (BCET) Imaging Geometry August 12, 2020 1 / 17

Human vision system
The human visual system consist of an eye that transforms light in to
the neural signals and create neural activity in the brain and extract
necessary information for human vision.
In human visual perception, the eyes act as the sensor or camera, neu-
rons act as the connecting cable and the brain acts as the processor.
The basic elements of visual perceptions are
Structure of Eye
Image Formation in the Eye
Brightnes Adaptation and Discrimination

Structure of Eye
The human visual system consist of an eye that transforms light in to
the neural signals and create neural activity in the brain and extract
necessary information for human vision.

Structure of Eye

Structure of Eye
The pupil allows light to enter the eye to fall on the retina. It contracts
when exposed to bright light and controls the amount of light entering
to eye.
A colored circular pigmented muscle called irish gives us our eye colour
and controls the size of the pupil so that appropriate amount of light
is allowed to enter the eye.
A transparent external surface called cornea covers both the pupil and
the irish. This is the ﬁrst and most powerful lens of the optical system
of the eye and together with crystalline lens, it allows the production
of a sharpe image at the retinal photo receptor level.
The upper white part of the eye is called sclera which form a supporting
wall of the eyeball. The sclera is a nearly spherical shell with a radius
of 11mm and 1mm thick.‘

Image formation in the eye
When the lens of the eye focus an image of the outside world onto a
light-sensitive membrane in the back of the eye, called retina the image
is formed. The lens of the eye focuses light on the photoreceptive
cells of the retina which detects the photons of light and responds by
producing neural impulses.
In an photographic camera, the lens has a fixed focal length and fo-
cusing at various distances is achieved by varying the distance between
the lens and the imaging plane.
In human eye the distance between the lens and the imaging region(retina)
is fixed, and the focal length needed to achieve proper focus is obtained
by varying the shape of the lens. The fibers in the ciliary body accom-
plish this by flattening or thickening the lens for distant or near objects.

Image formation in the eye
The distance between the center of the lens and the retina along the
visual axis is approximately 17mm and the range of the focal lengths
is approximately 14mm to 17mm.
Suppose that a person is looking at a tree 15m high at a distance of
100m. Let h denote the height of that object in the retinal image, then
from geometry we get the relation 15/100 = h/17 or h = 2.55mm

Brightness Adaptation and Discrimination:
Digital images are displayed as a discrete set of intensities. The eyes
ability to discriminate black and white at diﬀerent intensity levels is an
important consideration in presenting image processing result.

Electromagnetic spectrum:

Brightness Adaptation and Discrimination:
The range of light intensity levels to which the human visual system
can adapt is of the order of 1010 that is from scotopic threshold to
glare limit.
The intensity perceived by the human visual system(subjective bright-
ness) is a logarithmic function of the light intensity incedent on the
eye.
The long solid curve represents the range of intensities to which the
visual system can adapt.
For any given set of conditions the current sensitivity level of the visual
system is called the brightness adaption level which may correspond to
brightness Ba.
The short intersecting curve represents the range of subjective bright-
ness that the eye can perceive when adapted to level Ba. This range is
restricted up to level Bb and below which all stimuli are percieved as
black.

Photopic and Scotopic Vision
The two types of receptors responsible for human vision are rods and
cones. The rods are sensitive to very low illumination and are respon-
sible for night vision (scotopic vision).
The cones which are tightly packed in the fovea, lie inline with the
visual axis and are mainly responsible for color vision (photopic vision).
The minimum sensitivity of cones is of the order of a microlambert(mL)
The cones in the human eye can be devided in to three principal sensing
categories corresponding to red, green, blue.

Photopic and Scotopic Vision
The cones in each eye numbers between 6 to 7 million and are located
in the central portion of retina called fovea which are highly sensitive
to color.
The number of rods is much larger, between 75 to 150 million. Rods
serve to give a general overall picture of the ﬁeld of view and are
sensitive to low levels of illumination.
Objects appear coloured in daylight appears colourless in moon light
because only rods are stimulated. This phenomenon is known as sco-
topic vision.

Weber ratio
Weber ratio gives an measure of brightness discrimination that is the
ability of the eye to discriminate between changes in light intensity at
any speciﬁc adaptation level.
Weber ratio is deﬁned as the ratio of the increment of illumination(∆Ic)
discriminable 50 percent of the time to the background illumination I.
Hence
w =
∆Ic
I
A small value of w means that a small percentage change in intensity
is discriminable which represents good brightness discrimination. Simi-
larly large value of w means that a large percentage change in intensity
is required and represents poor brightness discrimination.

Machband eﬀect
The spatial interaction of luminance from an object and its surroundings
creates the Machband eﬀect, which shows that brightness is not a
monotonic function of luminance.
The intensity is uniform over the width of the bar. However the visual
appearance is that each strip is darker at its left side than its right.
Machbanding is caused by lateral inhibition of the receptors in the eye.
As the receptors recieve light, they draw light sensitive chemical com-
pounds from adjacent regions, thus inhibiting the response of receptors
in those regions.
Perceived intensity is not a simple function of actual intensity)

Machband eﬀect
Here all lines that are oriented at 450 are equidistant and parallel.

Machband eﬀect
The two horizontal line segments are of the same length.

Machband effect
The outline of a square is seen clearly, despite the fact that no lines
defining such a figure are part of the image.

Imaging geometry

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