Jag känner inte personen på bilden.

Here känner is the present tense of känna, which often means to know in the sense of to be acquainted with someone.

So Jag känner inte personen på bilden means that the speaker is not personally familiar with that person.

This is different from:

• Jag vet inte vem personen är = I don’t know who the person is
• Jag känner inte personen = I don’t know the person

Swedish often separates these ideas more clearly than English does.

Because Swedish uses different verbs for different kinds of know.

• känna = to know a person / be familiar with
• veta = to know a fact / have information
• kunna = to know how to / be able to

So:

• Jag känner Anna. = I know Anna.
• Jag vet svaret. = I know the answer.
• Jag kan simma. = I can swim / I know how to swim.

In this sentence, the object is a person, so känna is the natural choice.

In a normal Swedish main clause, inte usually comes after the finite verb.

So the pattern is:

• Jag känner inte personen.
• Hon bor inte här.
• Vi kommer inte idag.

That is why inte follows känner.

A very rough pattern is:

subject + verb + inte + rest

Personen is the definite form of person, meaning the person.

• en person = a person
• personen = the person

Since the sentence refers to a specific person, the definite form is used.

Swedish often adds the definite ending directly to the noun instead of using a separate word like the.

So:

• en bok = a book
• boken = the book
• en person = a person
• personen = the person

Because in Swedish, the definite article is often attached to the end of the noun as a suffix.

So English:

• the person

becomes Swedish:

• personen

You do sometimes see den/det/de with a definite noun, but usually when there is an adjective:

• personen = the person
• den unga personen = the young person

Without an adjective, personen by itself is enough.

Swedish usually says på bilden for in the picture / in the photo.

Even though English says in the picture, Swedish idiomatically uses på here.

So:

• på bilden = in the picture
• på fotot = in the photo

Using i bilden can mean something different in some contexts, and it is not the normal choice for identifying someone shown in a photo or image.

Bilden is the definite singular form of bild, meaning the picture / the image.

• en bild = a picture
• bilden = the picture

So på bilden literally looks like on the picture, but in natural English it corresponds to in the picture.

Yes. På bilden describes personen.

So the structure is:

• Jag = subject
• känner inte = verb + negation
• personen på bilden = object phrase

Here på bilden works like a description of which person we mean:

• personen på bilden = the person in the picture

It is similar to English phrases like:

• the man in the car
• the woman at the door
• the person in the picture

Not necessarily. The most natural meaning is that the speaker is not personally acquainted with the person.

So it usually means:

• I don’t know that person personally

It does not automatically mean:

• I can’t tell who that is

If you wanted to emphasize lack of identification, Swedish might more naturally say something like:

• Jag vet inte vem personen på bilden är. = I don’t know who the person in the picture is.

Not freely. In a basic statement like this, the normal order is:

Jag känner inte personen på bilden.

Swedish word order is fairly strict in main clauses. The finite verb usually stays in the second position, and inte typically comes after it.

So:

• Jag känner inte personen på bilden. = correct
• Jag inte känner personen på bilden. = not normal
• Jag känner personen inte. = not normal in ordinary modern Swedish

If another element comes first, the verb still stays second:

• Personen på bilden känner jag inte.

That version adds emphasis, roughly like The person in the picture, I don’t know.

The main stress usually falls on the most important information, often inte and/or the noun phrase at the end.

A natural rhythm might be:

Jag känner inte personen på bilden.

If the important contrast is the negation, inte may stand out more. If the key information is which person, then personen på bilden may receive more emphasis.

In normal speech, jag is often pronounced like ya rather than a fully careful jag.