Results of two-dimensional DWT

I am trying to understand the decomposition step of a two-dimensional DWT: https://www.mathworks.com/help/wavelet/ref/dwt2.html

In the Matlab explanation, the two-dimensional DWT generates 4 new images ( CA, CH, CV, and CD) that represent the approximation, the horizontal details, the vertical details and the diagonal details.

I am also reading the explanation about the two-dimensional DWT that can be found at the following link: https://mil.ufl.edu/nechyba/www/eel6562/course_materials/t5.wavelets/intro_dwt.pdf

But the author shows the results as LL, LH, HL and HH.

I want to know if it corresponds to the same thing as CA, CH, CV, and CD.

Is the following comparison correct?

• CA == LL == approximation
• CH == LH == horizontal
• CV == HL == vertical
• CD == HH == diagonal

I'm also a little confused about the LH and HL results. In some posts, I have read that the LH represents the horizontal details and in other, I have read that it represents the vertical details.

For example, as answered here , the user explains that:

" In the wavelet terminology, LL is the approxmation image, LH is the vertical details, HL is the horizontal details, and HH is the diagonal details."

But in this article the author says:

" The LL band corresponds roughly to a down-sampled (by a factor of two) version of the original image. The LH band tends to preserve localized horizontal features, while the HL band tends to preserve localized vertical features in the original image. Finally, the HH band tends to isolate localized high-frequency point features in the image."

Thanks