What if I don't mention I have liquids in my carry-on?

Yes the x-ray machines detect the liquids when scanning your luggage. Not taking the liquids out of your hand-luggage will not raise any issue in those countries in which it is not mandatory to do so. However, in the remaining countries, your luggage will either be placed on a separate conveyor belt coming out of the x-ray machine, or will be pointed at by the security officer manning the machine, and will be hand inspected by the airport security staff. Needless to say they will enforce the rules. Moreover, this will ensure you lose at least fifteen minutes of your time whilst all the checks are completed. The UK is one such country. Last time I flew out of EDI, there were signs explicitly stating that failure to remove liquids from hand-luggage would result in extra, and lengthy, security checks.

I will depend entirely on how the screener examining the x-ray image interprets that image. The shape of the container will appear though.

Worst case scenario: Your bag will be searched.

Next to worst case scenario: They will locate and remove just the suspicious item, but not search the entire bag.+

Shortly after the TSA liquid bad I had, just as you, a tube of toothpaste confiscated after a screener saw it on the belt, not in the x-ray.

After that, I just stopped taking my liquids out. The replacement was never confiscated.

+The screener charged with searching the bag will look at the image to learn the exact location of the item.

Here's my experience from a recent trip when I decided to hide my 125ml toothpaste tube:

RIX: had to go through extra security checks for some reason, but the toothpaste went unnoticed.

SFO: the toothpaste went unnoticed. So much for TSA.

FRA: they noticed it and threw it out while speaking angrily in German. That took about 5 minutes of extra time.

In conclusion, it seems you generally don't risk much by leaving your liquid in the bag.