In Theravada tradition, Kāliṅgabodhi Jataka (Jataka no. 479) recounts how the Buddha advised Ananda to plant Bodhi tree in front of the gate of Jetavana monastery so that people can show reverence to the Buddha when he is going around to teach Dhamma:
When the Tathagata had set forth on pilgrimage, for the purpose of gathering in those who were ripe for conversion, the citizens of Savatthi proceeded to Jetavana, their hands full of garlands and fragrant wreaths, and finding no other place to show their reverence, laid them by the gateway of the perfumed chamber and went off. This caused great rejoicings.
But Anathapindika got to hear of it; and on the return of the Tathagata visited Elder Ananda and said to him,—“This monastery, Sir, is left unprovided while the Tathagata goes on pilgrimage, and there is no place for the people to do reverence by offering fragrant wreaths and garlands. Will you be so kind, Sir, as to tell the Tathagata of this matter, and learn from him whether or no it is possible to find a place for this purpose.”
The other, nothing loth, did so, asking, “How many shrines are there?”
“Which are they?”
“Shrines for a relic of the body (sārirīka cetiya), a relic of use or wear (pāribhogika cetiya), a relic of memorial (uddesika cetiya)“
“Can a shrine be made, Sir, during your life?”
“No, Ananda, not a body-shrine; that kind is made when a Buddha enters Nirvana. A shrine of memorial is improper because the connection depends on the imagination only. But the great bo-tree used by the Buddhas is fit for a shrine, be they alive or be they dead.”
“Sir, while you are away on pilgrimage the great monastery of Jetavana is unprotected, and the people have no place where they can show their reverence. Shall I plant a seed of the great bo-tree before the gateway of Jetavana?”
“By all means so do, Ananda, and that shall be as it were an abiding place for me.”
It is the uddesika cetiya where the Buddha images or statues (Buddharupa) belong to. According to Jataka story quoted above, udessika do not have any physical connection to the Buddha, but still serve as objects of reverence because they were created in his memory. Originally udessika were secondary to pāribhogika and sārīraka, but with the influence of Greco-Buddhism, statues of the Buddha were produced in great numbers, followed later by paintings and other images. Nowadays, the Buddha statues become primary Buddhist objects of veneration.
In northern Buddhist tradition, the canonical source for veneration of Buddha images is found in Chinese Ekottarika Agama chapter 36 sutra no. 5 (EA 36.5). It recounts story of King Udayana (Pali: Udena) who fell ill because of he did not see the Buddha, who went to the Tavatimsa heaven to teach Dharma to his mother, for a long time. The king’s attendants made the king a five-foot-high sandalwood Buddha statue so that the king recovered from his illness. The Buddha then approved the statue as object of veneration for the future generation. According to Chinese Buddhist tradition, this is the first Buddha statue made in the Buddha’s lifetime and current models of Buddha statues are based on this first statue, but the historicity of this story is doubtful because there’s no archeological evidence that Buddha images is made in the Buddha’s lifetime.