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


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.


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.


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.


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.


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.


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.


A dog sitting on a couch.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
I'm not good at math so would you help me
what is the problem that i will help you to self with?
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele 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, Elec 301 projects fall 2014. OpenStax CNX. Jan 09, 2015 Download for free at http://legacy.cnx.org/content/col11734/1.2
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