# Python calculate centroid of vectors

I was wonder is there a perl or python module that could make my life easier when working with large datasets of lat long points? If you want to do this in Python I'd recommend the Shapely library. You could read all your points into a MultiPoint object, and every object in Shapley has a centroid property. A quick sample:. You might want to check out ESRI's help on working with geometry. You will want to use the Describe function and the shapeFieldName property. There are two properties for centroids that you can use. One is called centroid which is the true centroid if it is within or on the feature; otherwise, returns the label point returns a point object. The other is called trueCentroid which returns the centre of gravity centroid regardless of whether it is actually within the shape or not. Sign up to join this community.

The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. How should I go about calculating the centroid of several lat long points in python, and perl? Ask Question. Asked 7 years, 9 months ago. Active 7 years, 9 months ago. Viewed 6k times. Thank you for your time. Beau Bouchard Beau Bouchard 1 1 gold badge 4 4 silver badges 10 10 bronze badges.In middle school, we learned about various shapes in geometry. It was relatively easy to find the centers of standard shapes like the circle, square, triangle, ellipse, etc. But when it came to finding the centroid of an arbitrary shape, the methods were not straightforward. Some nerdy friends said it would require calculus.

Other practical friends suggested intersecting plumblines. The same problem of finding centroid is relevant when you work in Computer Vision — except, you are dealing with pixels instead of atoms! In this post, we will first discuss how to find the center of an arbitrarily shaped blob and then we will move to the case of multiple blobs.

### How to Find the Centroid in a Clustering Analysis

A blob is a group of connected pixels in an image that shares some common property e. If the shape we are interested in is not binary, we have to binarize it first.

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The centroid of a shape is the arithmetic mean i. Suppose a shape consists of distinct pointsthen the centroid is given by. In the context of image processing and computer vision, each shape is made of pixels, and the centroid is simply the weighted average of all the pixels constituting the shape.

We can find the center of the blob using moments in OpenCV. Image Moment is a particular weighted average of image pixel intensities, with the help of which we can find some specific properties of an image, like radius, area, centroid etc. To find the centroid of the image, we generally convert it to binary format and then find its center.

Finding the center of only one blob is quite easy, but what if there are multiple blobs in the Image? Well then, we will have to use findContours to find the number of contours in the Image and find the center of each of them. Let us see how it works! You can include, the below code snippet to prevent getting errors, this simply neglects the contours which are not segmented properly.

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What is a blob? What is the centroid of a shape? Steps for finding Centroid of a Blob in OpenCV To find the center of the blob, we will perform the following steps:- 1.

Convert the Image to grayscale. Perform Binarization on the Image. Find the center of the image after calculating the moments. Some of the functions may change according to your version. Download Code To easily follow along with this tutorial, please download code by clicking on the button below.

Download Code.Cluster analysis is a method of organizing data into representative groups based upon similar characteristics. Each member of the cluster has more in common with other members of the same cluster than with members of the other groups.

The most representative point within the group is called the centroid. Usually, this is the mean of the values of the points of data in the cluster. Organize the data. If the data consists of a single variable, a histogram might be appropriate. If two variables are involved, graph the data on a coordinate plane. For example, if you were looking at the height and weight of school children in a classroom, plot the points of data for each child on a graph, with the weight being the horizontal axis and the height being the vertical axis.

If more than two variables are involved, matrices may be needed to display the data. Group the data into clusters. Each cluster should consist of the points of data closest to it. In the height and weight example, group any points of data that appear to be close together. The number of clusters, and whether every point of data has to be in a cluster, may depend upon the purposes of the study. For each cluster, add the values of all members. For example, if a cluster of data consisted of the points 80, 5675, 5360, 50and 68,54the sum of the values would be Divide the total by the number of members of the cluster.

In the example above, divided by four is Plot the cluster centroids and determine whether any points are closer to a centroid of another cluster than they are to the centroid of their own cluster. If any points are closer to a different centroid, redistribute them to the cluster containing the closer centroid. Repeat Steps 3, 4 and 5 until all points of data are in the cluster containing the centroid to which they are closest.

If the centroid has to be a particular point of data instead of a midpoint between the data, then the median may be used to determine it, instead of the mean. Talmadge Walker is a former schoolteacher turned professional writer. He has a bachelor's degree from Birmingham-Southern College and a master's degree in special education from Elon University. Things You'll Need. About the Author.

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I have one list including sets of vectors, all with 3 coordinates. I need to get a new list that will include the average of the respective coordinates of these vectors, as per their teams. In particular, I have a list of lists of lists of numbers:. I have tried doing the above with a series of nested for loopsbut I keep loosing track of it and getting wrong results.

I am sorry if my problem is misstated, but I really could not find a better way to describe my situation. It is also using generators and map.

So basically map is receiving map mean, 1,1,10,1,0 in the first iteration. Map function calls the mean function once per element in the tuples passing one element from each tuple: mean 1,0mean 1,1 and mean 1,0 and then groups them in a map object which you can think is the same than the generator.

And remember all this was done for each element in the first level of the list. So we have a generator that will yield 3 map objects: one with mean 1,0mean 1,1 and mean 1,0 ; a second one with mean 0mean 0 and mean 2 and a last one with mean 1,2,2mean 1,2,2 and mean 1,2,1. The second step is applying the same function with the same map expresion once more so that we get a single map object with: mean mean 1,0 ,mean 0 ,mean 1,2,2mean mean 1,1 ,mean 0 ,mean 1,2,2 and mean mean 1,0 ,mean 2 ,mean 1,2,1.

By forcinf it to transform to a list we can print it in the console. If you are using Python 2. You need zip! Iterate through your input list, zip the sub lists, and then, for every element in zipped result, find the average! Note: If you are using python3 and above, you need not convert your integer to float explicitly while you divide.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up. When performing hierarchical clustering, one can use many metrics to measure the distance between clusters.

Two such metrics imply calculation of the centroids and means of data points in the clusters. What is the difference between the mean and the centroid?

Aren't these the same point in cluster? As far as I know, the "mean" of a cluster and the centroid of a single cluster are the same thing, though the term "centroid" might be a little more precise than "mean" when dealing with multivariate data. To find the centroid, one computes the arithmetic mean of the points' positions separately for each dimension. For example, if you had points at:. NB: The centroid does not have to be--and rarely isone of the original data points. The centroid is also sometimes called the center of mass or barycenter, based on its physical interpretation it's the center of mass of an object defined by the points.

Like the mean, the centroid's location minimizes the sum-squared distance from the other points. A related idea is the medoidwhich is the data point that is "least dissimilar" from all of the other data points. Unlike the centroid, the medoid has to be one of the original points. You may also be interested in the geometric median which is analgous to the median, but for multivariate data.

These are both different from the centroid. However, as Gabe points out in his answerthere is a difference between the "centroid distance" and the "average distance" when you're comparing clusters.

The average distance is calculated by finding the average pairwise distance between the points in each cluster. Centroid method first computes the average of each cluster within itself. Then it calculates one distance between those average points. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. How is finding the centroid different from finding the mean? Ask Question. Asked 7 years, 1 month ago.

Active 3 years, 10 months ago. Viewed 68k times. John Hoffman John Hoffman 1 1 gold badge 4 4 silver badges 6 6 bronze badges. Active Oldest Votes. NB: The centroid does not have to be--and rarely isone of the original data points The centroid is also sometimes called the center of mass or barycenter, based on its physical interpretation it's the center of mass of an object defined by the points. Matt Krause Matt Krause And also why the centroid is a good representative of a set of points?

You can imagine cases where they'll be the same, but in general, they will not. The centroid is "good" for the same reasons the mean is smallest sum-squared distance to the points and also has similar drawbacks e.

Gabe Gabe 41 1 1 bronze badge. I think you're talking about this part of the video? As far as I know, the centroid and mean of a single cluster are the same thing but, as you pointed out, the centroid distance and average distance between two clusters are different measures.Recall that the centroid of a triangle is the point where the triangle's three medians intersect. It is also the center of gravity of the triangle.

For more see Centroid of a triangle. The coordinates of the centroid are simply the average of the coordinates of the vertices.

Introduction to Centroid Full Basics with solve example in Hindi - Engineering Mechanics Lectures

So to find the x coordinate of the orthocenter, add up the three vertex x coordinates and divide by three. Repeat for the y coordinate. Use the calculator to calculate coordinates of the centroid of the triangle ABC. Enter the x,y coordinates of each vertex, in any order. In the interest of clarity in the applet above, the coordinates are rounded off to integers. This can cause calculations to be slightly off. Home Contact About Subject Index.

Given the coordinates of the three vertices of a triangle ABC, the centroid O coordinates are given by where A x and A y are the x and y coordinates of the point A etc. Try this Drag any point A,B,C. The centroid O of the triangle ABC is continuously recalculated using the above formula.

You can also drag the origin point at 0,0. Calculate Clear.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.

What is the way to calculate the centroid of polygon? I have a concave polygon of 16 points, and I want know the centroid of that. Now, using Pts as the vertices, I cut out a sided polygon, Jerome. This is not the same question. How can I ask it correctly?

### Find the Center of a Blob (Centroid) using OpenCV (C++/Python)

Consider 1 above. What has changed? I see two problems:. There are many concave polygons through 16 given points. Which did I cut out? I must uniquely identify the region area I want to measure. Here are two ways:. If a set of points are the vertices of a convex polygon, that polygon is unique.

Each convex region of Jerome is uniquely determined by its vertices. A unique perimeter is a unique polygon. Both ways allow me to draw the figure.

Note that the simple average mean does not distinguish order; it can't give the correct answer. Jerome is a plane figure: Its mass is proportional to area.