Hosea 3:4 is part of a brief "reprise" of the "prophet-as-symbol" in his relationship with an unfaithful woman/spouse. (The terms of their relationship and the connection between Hosea 1 and 3 are matters of discussion, even dispute, among interpreters.)
Here it appears to be part of a redemption scene, as the woman is taken into the prophet's home, now separated from the temptations to infidelity. The symbolic analogy is to Israel as "spouse", and the LORD in the role of the prophet.
OP's verse of interest, Hosea 3:4, comes in the context of the deprivation that leads to fidelity. It itemizes a number of aspects of Israel's corporate and religious life that that are to be deprived in order to induce the right orientation of people to God. Conveniently taken as three pairs, they will lack:
- king or prince
- sacrifice or maṣṣēbâ
- ephod or household god (teraphim)
OP's interest (as I understand it) is in the nature of the maṣṣēbâ, and what would it mean to go without it?
maṣṣēbâ (singular; maṣṣēbôt plural) is usually translated "standing stone" or the like; it is used 36× in the Hebrew Bible.
It is a stone pillar of some kind, used as a memorial stone or cult object;1 in the latter case it is usually associated with the male deity (typically baʿal in the context of Canaanite religion, while the asherah or wooden object was associated with the female deity).2
It is sometimes found as a "licit" object in the context of faithful worship of the LORD (e.g., Genesis 28:18, 22; Exodus 24:4; Isaiah 19:19). Far more often, however, it is proscribed and detested (e.g., Exodus 23:24; Deuteronomy 7:5; 12:3; 16:22; Micah 5:12; Ezekiel 26:11).
It is quite clear that Hosea's convictions fall into the latter category. The KJV's "image" as cited by OP is more commonly translated "[sacred] pillar, stone" or the like.
There is one other place in this small book where they feature -- Hosea 10:1-2 -- and it is worth noting for the light it sheds on Hos 3:4.
10:1 Israel is a luxuriant vine;
He produces fruit for himself.
The more his fruit,
The more altars he made;
The richer his land,
The better he made the sacred pillars.
2 Their heart is faithless;
Now they must bear their guilt.
The Lord will break down their altars
And destroy their sacred pillars.
The passage goes on to speak of kings, thus bringing together all the main elements also seen in the list of 3:4.
It is clear here in ch. 10 that the indictment is that any flourishing became associated with and devoted to the prohibited cult objects and promoted (in the point of view of the prophet) the perverse worship of the people. This false perception and devotion bring judgement in the form of the destruction of the place of worship. In this Hosea 3:4 finds a strong parallel in Hosea 10:1-2.
These elements of deviation from the worship of the LORD -- king, official cult, and domestic shrine -- will all be withrdrawn through the judgment of the LORD. The KJV's "image", more commonly "[stone] pillar", in particular represents an object that is associated with the male deity, and thus a particular offence in to the prophet who urges fidelity to the LORD who is not represented by any image whatsoever.
- The picture of the maṣṣēbâ is from the courtyard of the temple installation in Bronze Age Shechem = Tell Balata; it is no. 7 in the map at the link. The association with cult and altar is again seen.
- Canaanite religion had a variety of "gods" (male) and "goddesses" (female) in the pantheon. The pantheon typically had three generations of gods, the "high" god(s), the active gods, and the minor deities. Examples of each from Ugarit would be El & Asherah (the "high" god and goddess), Baal & Anat (an "active" god and goddess), though there are a good number more, and so on to the minor deities. See further Marvin Pope's Encyclopaedia Judaica article on Baal worship, and a brief piece by Mark Smith on the background of biblical "monotheism".