Visual Techniques

School of Computing, USM
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Date : November, 2017
Location : USM
Presented by:
Md. Shohel Rana
Instructed by:
Dr. Parthapratim Biswas
VISUAL TECHNIQUES

CONTENTS
• Motivation and Contribution
• What is Visual Techniques
• Applications
• Problem Definition
• Result and Discussion
• References
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MOTIVATION AND CONTRIBUTION
• Developing visual material can help to recall memory and also be a
quick way to show lots of information.
• Visualization helps us remember (like when we try to picture where
we’ve parked our car, and what's in our cupboards when writing a
shopping list).
• We can create diagrams and visual aids depicting module materials
and put them up around the house so that we are constantly
reminded of our learning.
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WHAT IS VISUAL TECHNIQUES
• Visual techniques offer an interesting, stimulating and interactive
approach to gathering information. They are appropriate in a variety
of situations, as they fulfil numerous functions.
When should it be used?
• Visual techniques can be used in many settings, as an alternative to
more traditional methods and may be particularly useful as:
 Pictures and graphs can help suggest opinions and allow the use of
imagination in expanding on a scene.
 Offering an alternative to traditional discussion groups, yet still being able
to draw out the rich variety of qualitative information from participants.
 A method of producing tangible outcomes at the end of the research
process (e.g. series of community generated impacts illustrating how
local people view the local area).
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PROBLEM DEFINITION
• Problem 1:
A.Write a short program to generate data points for displaying the
curve y = x2. Plot the data.
B.Add noise to y data points generated above by y0 = y + r s, where r is∗
a random number between 1 and 1 and s is a scaling factor that
controls the strength of the noise. Choose s appropriately to generate
noise and plot the data set.
C.Write a simple ﬁlter program by averaging the data points to smooth
the plot in B. You may use any programming languages and ready
made random number generators but not inbuilt smoothing
programs. Investigate the relationship between the strength of the
noise and the number of times you need to run the ﬁlter program to
smooth the noisy data set.
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PROBLEM DEFINITION (CONT.)
• Essential in the collection of data taken over time is some form of random
variation. Having many methods for reducing of canceling the effect due to
random variation. An oftenused technique in industry is "smoothing". This
technique, when properly applied, tells more clearly the essential
movement, periodic and cyclic components
• Smoothing data removes random variation and shows trends and cyclic
components taking averages is the simplest way to smooth data
• There are two distinct groups of smoothing methods
 Averaging Methods
 Exponential Smoothing Methods
• We examined averaging methods, such as the "simple" average of all past
data
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• In summary, we state that
 The "simple" average of all past observations is only a useful estimate for
calculating when there are no trends. If there are trends, use different estimates
that take the trend into account
 The average "weighs" all past observations equally. For example, the average of
the values 3, 4, 5 is 4. We know, of course, that an average is computed by
adding all the values and dividing the sum by the number of values. Another way
of computing the average is by adding each value divided by the number of
values.
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• Problem 2:
A.Write a short program to generate N uniform random variates x
between -1 to +1 in one dimension. Compute the histogram of the N
variates and visualize your data.
B.Repeat the calculation in two dimension.
C.Using the uniform random variates x, construct new variates y, such
that
where m is an integer > 5. Find the distribution (i.e., histogram) of y and plot
your results in two dimension.
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• A Histogram is a vertical bar chart that depicts the distribution of a set of
data. Unlike Run Charts or Control Charts, a Histogram does not reflect
process performance over time.
• A Histogram will make it easy to see where the majority of values falls in a
measurement scale, and how much variation there is.
• When are Histograms used?
 Summarize large data sets graphically
 Compare process results with specification limits
 Communicate information graphically
 Use a tool to assist in decision making
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• Problem 3:
A.Download the file ‘data.jpg’.
B.Digitize the plot using a digitizing software and save the data in a file.
C.De-convolute the data using a linear combination of gaussian functions as
follows:
Write
where jmax is the number of gaussian functions defined by the parameters σj and xj.
 Form the deviation L^(2) (or its square) as discussed in the class:
• Fit L^(2) w.r.t the gaussian parameters above using your favorite fitting program.
• Plot the original and fitted data. Show also the individual gaussian functions and the
fitted data in a separate plot.
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• Given a large number of data points, we may sometimes want to figure out
which ones vary significantly from the average. For example, in
manufacturing, we may want to detect defects or anomalies. We show how
a dataset can be modeled using a Gaussian distribution, and how the
model can be used for anomaly detection
• The Gaussian distribution is a continuous function which approximates the
exact binomial distribution of events
• The signal error if often a sum of many independent errors. For example, in
CCD camera one could have photon noise, transmission noise, digitization
noise that are mostly independent, so the error will often be normally
distributed due to the central limit theorem.
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• Distribution fitting involves modelling the probability distribution of a single
variable. The model is a normalized probability density function. The
appropriate plot for the data is a histogram
• The normal distribution is a theoretical function commonly used in inferential
statistics as an approximation to sampling distributions. In general, the
normal distribution provides a good model for a random variable, when:
 There is a strong tendency for the variable to take a central value;
 Positive and negative deviations from this central value are equally likely;
 The frequency of deviations falls off rapidly as the deviations become larger.
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• Problem 4:
Consider a triangle represented by three vertices v1, v2 and v3 in a plane.
Write a program to compute the center and radius of the circumcircle of
the triangle. This result will be useful in constructing the Delaunay
triangulation of a set of points in two dimensions.
• Problem 5:
a.Generate a set of points P = {xn, yn} on a plane using a random number
generator so that (xn, yn) [0,L] and the distance between any two points is∈
always greater than r0. Choose, for example, n = 100, L = 10 and r = 1.
b.Using MATLAB, write a program to generate Delaunay triangulation of the
set.
• Problem 6:
Repeat problem 5(b) using the DL algorithm discussed in the class.
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• A technique for creating a mesh of contiguous, nonoverlapping triangles
from a dataset of points. Each triangle's circumscribing circle contains no
points from the dataset in its interior. Delaunay triangulation is named for the
Russian mathematician Boris Nikolaevich Delaunay
• The Delaunay triangulation is a triangulation which is equivalent to the nerve
of the cells in a Voronoi diagram, i.e., that triangulation of the convex hull of
the points in the diagram in which every circumcircle of a triangle is an
empty circle
• Delaunay triangulations help in constructing various things:
 Euclidean Minimum Spanning Trees
 Approximations to the Euclidean
 Traveling Salesperson Problem
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• Problem 8:
Generate a set of points P = {xn, yn} on a plane using a random number
generator so that (xn, yn) [0,L] and the distance between any two points is∈
always greater than r0. Choose, for example, n = 300, L = 30 and r0 = 1.
Construct the Voronoi diagram for this point set using:
a.the circumcenters of the DL triangles
b.the points of intersection of the perpendicular bisectors of the lines joining
the nearest neighbors of each point
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• Problem 7:
Generate a set of points {xn, yn} in a plane and construct the convex hull of
the set. Vary n = 500 to n = 10000 in steps of 500 and plot a graph showing
the CPU time versus number of points in the set.
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• Why Convex Hulls?
 shortest path avoiding the obstacle
• Applications:
 Image Registration and Retrieval
 Image Classification
 Uses of convex-hull in Image Editing Softwares i.e. photoshop
 Magic-wand Tool
 Glow & shadow Effect on layer. Can be better understand by applying on non-rectangular image.
 Make a selection by ctrl+click on layer.
 Use of convex hull algorithm in daily life by our Mom.
 Gathering grain seeds on the floor by hand or using whipper
 Use of convex hull algorithm by weather professionals to determine area of rain fall.
 Determine total area of waterfalls by analyzing all censors those send signal of waterfall using
convex hell algorithm
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• Problem 9:
Generate a set of points {xn, yn} in a plane and implement the k-means
cluster algorithm to partition data points into k clusters. Check your results by
generating points from a Gaussian random distribution centered at different
points in the plane. Compute also the radius of gyration of each cluster and
present your results in a 2-dimensional plot for visualization.
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• K-Means clustering generates a specific number of disjoint, flat (non-
hierarchical) clusters. It is well suited to generating circular clusters.
• The K-Means method is numerical, unsupervised, non-deterministic and
iterative
• k-means becomes a great solution for pre-clustering, reducing the space
into disjoint smaller sub-spaces where other clustering algorithms can be
applied
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• The K-Means Algorithm Process
1. The dataset is partitioned into K clusters and the data points are randomly
assigned to the clusters resulting in clusters that have roughly the same number
of data points.
2. For each data point:
3. Calculate the distance from the data point to each cluster.
4. If the data point is closest to its own cluster, leave it where it is. If the data point is
not closest to its own cluster, move it into the closest cluster.
5. Repeat the above step until a complete pass through all the data points results
in no data point moving from one cluster to another. At this point the clusters
are stable and the clustering process ends.
6. The choice of initial partition can greatly affect the final clusters that result, in
terms of inter-cluster and intra-cluster distances and unity.
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RESULT AND DISCUSSION
What we learnt from this course?
 How to look on problems?
 Where we can apply these methodologies?
 How to solve related problems using these methodologies?
 How to summarize results?
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QUESTION?
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