Obrada slike traje kratko.

Because slike is in the genitive singular.

In obrada slike, the noun obrada means processing, and Croatian commonly uses the genitive after nouns like this to show what is being processed:

• obrada slike = processing of the image / image processing
• obrada podataka = processing of data
• obrada teksta = processing of text

So slika is the basic dictionary form, but after obrada you need slike.

Slike is genitive singular.

It appears because obrada is a noun, and Croatian often links two nouns by putting the second one into the genitive case. This is similar to English of:

• obrada slike = processing of the image
• literally: processing image-GEN

So this is a very common noun + genitive pattern.

Traje is the 3rd person singular present tense of the verb trajati, which means to last, to continue, or to take time.

Here it agrees with the subject obrada slike, which is singular:

• Obrada slike traje... = Image processing lasts / takes...

Other forms of trajati include:

• trajem = I last
• traješ = you last
• traje = he/she/it lasts
• trajemo = we last
• trajete = you (plural) last
• traju = they last

Because kratko is an adverb here, not an adjective.

It modifies the verb traje:

• traje kratko = lasts briefly / lasts a short time

If you used kratka, that would be an adjective agreeing with obrada:

• obrada je kratka = the processing is short

That sentence is possible, but it is a different structure. In your sentence, Croatian prefers the adverb with trajati:

• traje kratko = more natural for duration

Not exactly word-for-word, but that is the idea.

In Croatian, kratko can function as an adverb meaning something like:

• for a short time
• briefly
• shortly in the sense of duration

So traje kratko means it does not last long.

A more expanded version would be:

• Obrada slike traje kratko vrijeme. = Image processing takes a short time.

Very often, vrijeme is simply omitted because the meaning is already clear.

Yes, absolutely.

Both are possible:

• Obrada slike traje kratko.
• Obrada slike traje kratko vrijeme.

The shorter version sounds more natural in many contexts because Croatian often leaves out words that are understood already. The longer version is a bit more explicit.

Because Croatian has no articles.

So a sentence like Obrada slike traje kratko can mean, depending on context:

• Image processing takes a short time
• The processing of the image takes a short time
• Processing an image takes a short time

Croatian relies on context instead of articles such as the and a/an.

The basic order here is natural and neutral:

• Obrada slike traje kratko.

But Croatian word order is more flexible than English, so other orders are possible for emphasis, for example:

• Kratko traje obrada slike.
• Traje kratko obrada slike.

These sound more marked or stylistic. For a learner, the safest and most natural version is the original one.

It can mean both, depending on context.

Grammatically, it is literally:

• processing of the image

But in many real situations, especially technical ones, it works very naturally as:

• image processing

So if this appears in a computing or technical context, obrada slike is often best understood as image processing.

Yes.

The noun slika can mean several related things in English, such as:

• image
• picture
• sometimes painting, depending on context

So obrada slike could be interpreted as:

• image processing
• picture processing

In technical language, image is usually the best choice.

It is grammatically correct, but it does not sound as natural in the same way.

• Obrada slike traje kratko. focuses on duration and is the normal way to say it.
• Obrada slike je kratka. describes the processing itself as short, which is understandable, but less idiomatic in many contexts.

Croatian often uses trajati + adverb/expression of time when talking about how long something lasts.

Obrada is a feminine noun.

You can tell from its ending -a in the basic form, which is very common for feminine nouns in Croatian. That is why, if you used an adjective with it, the adjective would also need feminine singular agreement:

• kratka obrada = short processing

In your sentence, however, the word connected to duration is not an adjective modifying obrada, but the adverb kratko modifying traje.