What is difference between "orientation" of Regionprops and "principal component coefficients" of PCA

Hi

I am stuck in my work because of few confusions.

1. Is the difference of "principal component coefficients" of PCA and "orientation" of regionprops? Do they give the same result?

2. In PCA, By default, pca centers the data and uses the singular value decomposition (SVD) algorithm. But what if I use regionprops to get orientation? Is that on centered data as well?

Can anyone clarify please?

Answer 1

[Image Analyst]

The orientation fits an ellipse to the blob and gives you the angle of the major axis. PCA (demo attached) gives the PCs of the data not the angle. Of course PC1 will align with the major axis but the PC1 values themselves are the values of the image along the PC1 direction. So for a megapixel binary image you'd get a million floating point values that are the binary image interpolated at the new locations in PC-space.

Think of a color image with a gamut that looks like a long cigar if you were to do a scatterplot of the color values. now PC1 would be along the long axis of the cigar. PC1 is the major axis of the rotated coordinate system. PC2 and PC3 are the short axes perpendicular to the main cigar axis. So the new PC1 value is a linear combination of the red, green, and blue values. It's basically a gray level, not an angle like orientation from regionprops is.

[Ashbub]

Thankyou for your reply and the file.

For an irregular shape like the one shown here, what I understand, PC1 and Orientation will not be in the similar direction because of the way they are calculated.

As I am working with separated voids between sand particles, I will get similar type of shapes frequently. For 2D shapes I have already figured out the PC1 as shown by arrows on each particle in the attached file (PCA in 2D). It looks to me, Principal component (PC1)instead of major axis direction (Orientation from regionprops) will make more sense to get the direction of such shapes. Am I correct?

It that is true, now the problem is how to get PC1 for 3D objects of shapes like the similar shown here. Please suggest.

[Image Analyst]

Why don't you calculate each and plot them over the blobs and see which you agree with more overall?

[Ashbub]

Thankyou. I am considering this.