Diaptera wings classification using Topological Data Analysis

1 Introduction

Falar sobre o dataset, TDA, etc.

2 Methods

All images are in the images/processed directory. For each image, we load it, apply a gaussian blur, crop and make it have 150 pixels of height. The blurring step is necessary to “glue” small holes in the figure and keep it connected.

Source: Article Notebook

2.1 Vietoris-Rips filtration

We select 500 points from each image using a farthest point sample method

We then calculate its persistence diagrams using the Vietoris-Rips filtration etc.

We create the 1-dimensional persistence image for each persistence diagram using 10x10 matrices

2.2 Examples

Below are some examples of 1-dimensional barcodes, its persistence image and the original wing that generated it. Note: we are plotting the barcode using the birth and persistence.

We now calculate the Euclidean distance between each persistence image (seen as a vector of \(\mathbb{R}^{10x10}\)) and plot its heatmap

2.3 Persistence Homology Transform

Now we will create several filtrations based on points and lines, etc.

We start with the point (0, 0). Its filtration is the following

with corresponding sublevel barcode as

or, with persistence in the y-axis:

Let’s see step-by-step of this filtration:

Due to noise, some connected components are born in 0.2 and die only at 0. But the loops seems alright.

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