Well, we can't be sure if the painter of the picture is well versed in Scriptures or that he has drawn the positions of various Gods exactly as depicted in our Shastaras.
However,one get a good summary of the positions of Gods,Rishis,Vedas etc in a Cow's body in the "Grihasta Ashrama" chapter found in the Skanda Purana.
Cows standing for virtues do fall in the care of Brahmanas as the former represent Vedas-Rig Ved being the back of Cows, Yajur Ved being their middle portion, and Sama Ved their ‘Kukshi’(stomach); ‘Ishta’or Yagnas and Yagas and ‘Apurti’ or Wells, Tatakas, Gardens etc are their horns; Veda Suktas are the body hairs; Shanti Karma and Pushti Karma are their dung and urine; ‘Aksharas’ are their feet; Cows live for their Pada-Krama-Jata-and Ghana Paatha viz. the various Mantras; Swahakar, Swadhakar, Vashatkar and Hanthakar are the four nipples of their breasts, each of the nipples representing Devatas; Pitras; Bhutas, Rishis, Munis and Sureswaraganas; and Human beings respectively. The last nipple yeilds maximum milk to human beings.Thus the responsibility of looking after cows is squarely on human beings
The above words are those of Maharshi Vyasa as told to Yudhishtira.