in the above code we first checked in if condition whether the root category has sub categories or not.
Then if it contains, in foreach loop we loaded categories one by one. Afterwards in the loop at the statement
we are loading the category from the 'catalog/category' with the id and then in if condition we are checking for the attribute value $cat->getThumbnail().
If it contains the value then using the thumbnail attribute we get the image from the path and assign it to the variable $imageUrl. In the parameter $imageResized we will load the path of the resize images where those resized images will get saved.
Now, we created an object of the $imageUrl as $imageObj, then by using the same object we apllied the functions of resize properties of the image.
In this statement $imageObj->resize( 350, 450 ); we passed the aspect ratio of the image as height and width. the aspect ratio is one in which we desire to resize the image.
Now in the statement $imageObj->save( $imageResized ); we saved the resized image at the new path which we loaded in the parameter $imageResized.
So, now whenever we are required to display the resized thumbnail image of that aspect ratio of the categories we can assign the path new path to load those images as,