Relative and absolute poverty

I've never understood the notion of absolute poverty, as opposed to relative poverty. The absolute poverty rate is defined by Wikipedia as quantifying "... the number of people below a poverty threshold, and this poverty threshold is independent of time and place. For the measure to be absolute, the line must be the same in different countries."

But what is it that is absolute about absolute poverty? As I understand it, absolute poverty is calculted using a basket of goods type of argument: if you can't afford to buy enough to feed yourself (say) you're absolutely poor. But the amount and quality of food which counts as "feeding yourself" changes with time and place. How much is enough? Raw calories? Enough protein? Fresh fruit and vegetables? The first two were a luxury until recently, the fact that they're now regarded as things everyone should be able to afford is an inherently relative concept. Most people can afford to obtain them, so you are poor if you cannot.

What of education for your child? I suppose being unable to buy books or send your child to school would count as absolute poverty (if education was private, and formed part of the basket of goods and services). But again, these are things which were a luxury not too long ago and still are in many places. So why do we draw the line where it is, and not at say access to violin lessons or playing fields or small class sizes?

My point is that the notion of poverty is inherently relative. The absolute poverty line is determined by social convention, implcitly relative to what others in society can afford. How large a gap is tolerated between those at the poverty line and the median, or some higher rank position, is convention and nothing else. Surely all poverty is relative, or am I missing something?