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Introduction

The Scale- Invariant Feature Transform is an algorithm in computer vision to detect and describe points of interest in an image.

Approach

According to Prof. Dowe’s paper on Distinctive Image Features from Scale-Invariant Keypoints(2004), there are four stages to SIFT:

  1. “Scale-space extrema detection”- Searches the entire image for candidate interest points
  2. “Keypoint localization”- Calculate the location and scale for each candidate, remove candidates that are not stable
  3. “Orientation assignment”- Assign each key point with one or more orientations that are calculated based on the gradient direction at that key point location in the image
  4. “Keypoint descriptor”- For each key point, calculate the gradient in its surrounding area. This allows the transform to be distortion resistant. The above approach “transforms image data into scale-invariant coordinates relative to local features”.

Our project seeks to achieve scale, rotation and translation resistance. However due to time-constraint, we did not implement stage 4 “Keypoint descriptor” of SIFT.

Implementation

Stage 1

Apply Gaussian filters of different scales to the image. By using different scales the Gaussian filters would have different variances. Due to the inherent properties of Gaussian filters, this would “smooth” out the images, removing finer details of the image. At different scales, the details of the image that are insignificant compared to the standard deviation of the Gaussian filter applied would be removed. The Gaussians are generated using the following formula:

Gaussian Generation.

Then the image, represented as an array of digits, is convolved with the Gaussian.

Gaussian.

L(x,y,sigma) is the value of the resulting image at location (x,y) under the Gaussian filter with standard deviation sigma. I stands for the original image.

We applied Gaussians with scale 0, 1, and 2 to the image. At scale 0, we are essentially preserving the original image, at scales 1 and 2 we are “smoothing out” the image to an increasing extend. We have 3 octaves of resulting images, each octave consists of images resulting from repeated applying the gaussian filter of the same scale to the original image. After each octave, the image is down-sampled by two.

Code

A dog sitting on a couch.

Stage 2

Now we have the image smoothed to different extends, with variant amount of fine detailed preserved in the resulting images. Within each octave, we use Difference of Gaussian, which is basically subtracting neighboring images from each other. Difference of Gaussian is proven to be a close approximation of scale-normalized Laplacian of Gaussian, which is shown to "produce the most stable image features compared to a range of other possible image functions, such as the gradient, Hessian, or Harris corner function”. Moreover, Difference of Gaussian is efficient to compute since it’s just subtracting images.

Code

A dog sitting on a couch.

Then for each pixel in a resulting image, we compare it to its eight neighboring pixels in the same image and nine neighboring pixels in the images processed by adjacent scales. It’s selected if it’s greater or smaller than all its neighbors. The result is a candidate key point.

Code

A dog sitting on a couch.

Stage 3

To calculate the magnitude and orientation of each key point, we look at all it’s neighboring pixels in the image that is processed with the same scale.

A dog sitting on a couch.

m(x,y) stands for the gradient magnitude of the point and theta(x,y) stands for the orientation of the point.

Code

A dog sitting on a couch.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, A comparison of object recognition using the hough transform and the properties of moment of inertia. OpenStax CNX. Dec 16, 2014 Download for free at http://legacy.cnx.org/content/col11727/1.4
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