calculating eigenvalue of an image-CodePudding

I have some images and would like to look at the eigenvalues of the images (as image is a matrix). My issue is that the image is in the shape of TensorShape([577, 700, 3])

How can I possibly to some preprocessing to be able to have its eigen decomposition?

My try:

import tensorflow as tf
import numpy as np
from numpy import linalg as LA
import matplotlib.pyplot as plt


image_path = tf.keras.utils.get_file('YellowLabradorLooking_new.jpg', 'https://storage.googleapis.com/download.tensorflow.org/example_images/YellowLabradorLooking_new.jpg')
image_raw = tf.io.read_file(image_path)
image = tf.image.decode_image(image_raw)
image = tf.cast(image, tf.float32)
image = tf.image.resize(image, (224, 224))

LA.eig(image)

CodePudding user response：

If you have n images, and if images are of the same size, and if images are somehow centered, then you may consider that images are samples from a distribution, and you can use eigenvalue decomposition to study how different pixels in the image vary across the collection.

In this situation: say you have a collection of n [H,W] images. You can flatten images and form a [H*W, n] matrix. If the images are RGB, it can be a [H*W*3, n] array -- i.e. each pixel location and each color channel is treated as an independent dimension.

Eigenvalue decomposition will give you a collection of H*W*3-dimensional vectors, which can be reshaped back into RGB images. Getting all eigenvectors is going to be impossible (H*W*3*H*W*3 is usually huge), however calculating top 3-5 eigenvalues and eigenvectors shouldn't be a problem even if HxWx3 is large.

You can find a more detailed description searching for "Eigenfaces"; e.g. opencv-eigenfaces-for-face-recognition, wikipedia, classic CVPR91 paper, etc.

CodePudding user response：

A grayscale image can be (and usually is) represented as a matrix. A colored image can not. It is represented using three matrices, one for each color channel.

This is the problem with your code snippet. la.eig() expects a square array, or an array containing square arrays in its final two axes, but got an array of shape (224, 224, 3).

To fix this, you can shift the two 224 axes to the end using the np.rollaxis() function. The eigenvalues and -vectors will be calculated separately for each color channel.