You can use whichever dimension the bounding box is bigger in to figure out whether to split the box vertically or horizontally
@ivyn From my understanding it is not the bounding box that we are to split in this example. To split a box should be spatial partition, in which you partition space into non-overlapping regions. In this specific case we are doing object partition that split the objects rather than boxes. With object partition we may also get overlapping bounding boxes for each set of objects.
Actually in following slide (p80) we can see an example in which split the objects in bounding box by dimension of bounding box can be a bad partition as it can produce large empty space and overlapping bounding boxes (which can be avoided).