# Finding Affine Transform with Linear Least Squares



linear least squares is a method of fitting a model to data in which the relation between data and unknown paramere can be expressed in a linear form.
$$Ax=b$$
$$X^{*}= \underset{x}{\mathrm{argmin}}= \|Ax-b\|^{2} =(A^{T}A)^{-1}A^{T}b$$

And testing the code:

# Examples of Dynamic Programming with C++ and Matlab

In this tutorial, I will give you examples of using dynamic programming for solving the following problems:

1)Minimum number of coins for summing X.

2)The most (least) costly path on a grid (dynamic time warping).

3)Levenshtein edit distance.

4)Seam Carving. I have written a tutorial on that here and the recursive part is in the following lines:

The examples are taken from “Competitive Programmer’s Handbook” written by Antti Laaksonen.

# Peak Signal-to-Noise Ratio (PSNR) in Image using OpenCV and Matlab



Peak signal-to-noise ratio (PSNR) shows the ratio between the maximum possible power of a signal and the power of the same image with noise. PSNR is usually expressed in logarithmic decibel scale.

$$MSE =1/m*n \sum_{i=0}^{m-1} \sum_{j=0}^{n-1} [ Image( i,j) -NoisyImage( i,j) ] ^2$$
$$PSNR =10* \log_{10} \Bigg(MAXI^2/MSE\Bigg)$$

MSE is Mean Square Error and MAXI is the maximum possible pixel value of the image. For instance if the image is uint8, it will be 255.

Ref [1],[2], [3], 4

# Seam Carving Algorithm for Content-Aware Image Resizing with Matlab Code

Seam carving is an algorithm for resizing images while keeping the most prominent and conspicuous pixels in the image. The important pixels in an image are usually those who are located over horizontal or vertical edges, so to throw away some pixels we first find horizontal and vertical edges and store their magnitude as pixel energy. Then we use dynamic programming to find a path which contains the minimum energy level and we drop those pixels. We iteratively do this until we got our image in the desired size.

our image is 720×480,

let’s drop some rows and resize it to 640×480:

we can drop some columns and resize it to 720×320:

# Hierarchical Clustring in python



Hierarchical Clustering is a method of clustering which build a hierarchy of clusters. It could be Agglomerative or Divisive.

1. Agglomerative: At the first step, every item is a cluster, then clusters based on their distances are merged and form bigger clusters till all data is in one cluster (Bottom Up). The complexity is $$O (n^2log(n) )$$.
2. Divisive: At the beginning, all items are in one big cluster. Then iteratively we break this cluster into smaller clusters (Top Down). The complexity is  $$O (2^n)$$.

To merge or divide the clusters we need to know the shortest distance between clusters. The common metrics for the distance between clusters are:

• Single Link: smallest distance between points.
• Complete Link: largest distance between points.
• Average Link: average distance between points
• Centroid: distance between centroids.

Depending on the definition of ‘shortest distance’ (single/ complete/ average/ centroid link   ) we have different hierarchical clustering method.

Hierarchical Algorithms:

1. Single Link: at each iteration, two clusters that have the closest pair of elements will be merged into a bigger cluster.
2. Average Link: distance between clusters is the average distance between all points in between clusters. Clusters with the minimum of these distances merge into a bigger cluster.
3. Complete Link: distance between clusters is the distance between those two points that are farthest away from each other. Two clusters with the minimum of these distances merge into a bigger cluster.
4. Minimum spanning tree (MST): In a connected graph without any cycle, a spanning tree is a subset tree in which all vertex are still connected. If edges have weight, MST is a span tree in which the edges have the minimum weight. MST may not be unique.

to visualize the outcome of the hierarchical clustering we often use “Dendrogram”.

The following graph represents the following matrix :

Minimum spanning tree of the graph.

# Creating Virtual Directory in Apache

Usually, I write about robotics, computer vision and machine learning in this website but today I decided to make back of my website in my PC and I felt it’s not bad ti know a bit about XAMPP and especially Apache.

2) Then edit “/opt/lampp/etc/httpd.conf” and uncomment the line:

4) Then edit “/etc/hosts” and add:

5) Now create the index.php file inside “/home/behnam/ros-developer.com” and put the following inside:

6) Run:

# Connecting PS4 Controller dualshock via Bluetooth in Ubuntu

PS4 controllers work out of the box in Ubuntu with USB cable but I was looking for a way to get it work via Bluetooth as well. After installing a couple of packages I found “ds4drv”.
To install it:

Then you have to either add the user to the list of root user or simply run it with sudo:

Now hold ps button and share button on the controller and you should see the following in your terminal:

To check the button and see if everything is okay jut install jstest-gtk

# Maximum likelihood estimation explained

In this tutorial, I explain the “Maximum likelihood” and MLE (maximum likelihood estimation) for binomial and Gaussian distribution.