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This module carries instructions to correctly identify and match the images from the database.

Give me your digits!: identification algorithm

Feature extraction

In general

Now that the image is in the format of the database (28 x 28 grayscale), a method to match the image to the database must be explored. To achieve a high accuracy rate in matching from the database, a feature extraction method could be employed. Three methods will be explored: pixel matching, Principle Component Analysis (PCA), and two-dimensional Fast Fourier Transform (2D FFT).

Pixel matching

Pixel matching, the first method, is not to use any feature extraction. It is meant to match the image to the database in the most obvious manner. The identifier literally compares the images pixel by pixel and computes the mean squared error (MSE, sums up all the error). In fact, the following two methods employ pixel matching after the transforms.

Pca principle component analysis

Next, the Principle Component Analysis, employs an orthogonal linear transformation that transform the matrix to a new matrix such that the greatest variance of the projection of the data comes to the first coordinate (principle component), and the second highest variance to the second coordinate, and so on. For our purposes of matching the image from the database, the PCA actually performs very poorly. This is due to the fact that because the images so closely resemble each other (same variance). This similar variance is attributed to it being so small (28 x 28) and gray scale. As a result, the PCA transform of the images are almost identical for this specific database. Experimentally, roughly a 30% matching rate was observed, which is barely better than random guessing. PCA would be much better suited for large images with great variances.

2d fft

Last, our method of choice, is the two-dimensional Fast Fourier Transform. Recall that the FFT is a form of Discrete Fourier Transform. The 2D FFT, for our purpose of image extraction, is the a frequency representation of the images. Note that the magnitude of the FFT must be used to compute the MSE. Also, the Matlab fftshift command was used shift the high frequency to the center.

The formatted images and their 2D FFT’s

Identification

In general

Once the input images are transformed, they are now ready to be matched and identified by the images in the database. Three algorithms can be used: a) finding the lowest MSE, b) finding the best averaged MSE, and c) finding the highest frequency digit from the best one hundred MSE.

Absolute nearest neighbor

The first algorithm finds the database image that has the lowest MSE from the input image out of all the randomly selected database images and declares that the input image is the digit the matched database image represents. In other words, it is an absolute nearest neighbor approach. The accuracy of this method depends heavily on the number of randomly selected database images since the bigger the database to choose from, the higher the chance that there will be a perfect match.

Averaging database per digit

Another algorithm that could be used is to average all of the MSE’s of the database of one digit with a input digit,and declare the digit with the lowest average as the input’s digit. This method, in theory, should eliminate the chance picking an outlier.

Majority of nearest neighbors

Finally, the last algorithm is a variation of the aforementioned minimum MSE approach. This method picks the one hundred lowest MSE’s observed from the selected database and tallies the frequency of digits represented and declares the highest frequency digit is the input’s digit. In other words, it is finding the digit with the most nearest neighbors. In theory, this approach should be more associated with finding common features since higher frequency of certain digit means shared characteristics. A drawback of this method could come from a particularly poor input (say a 3 that looks awfully like an 8), there is a possibly of “tying” since the digits are separated by integers.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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
How can I make nanorobot?
Lily
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
how can I make nanorobot?
Lily
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
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Source:  OpenStax, Elec 301 projects fall 2008. OpenStax CNX. Jan 22, 2009 Download for free at http://cnx.org/content/col10633/1.1
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