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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
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A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
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David
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emma Reply
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Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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Adjanou
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Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
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Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo 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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