Late Spring

I was just watching Late Spring by Ozu and there is a line of English translation I don't understand the meaning of. After Noriko declines the invitation to the concert Hattori says:
Pickled radish strung together?
To which Noriko replies:
Yes. My blade must be getting dull.
Surely this is a literal translation and the meaning lies elsewhere. Does anyone know what the equivalent English saying is? The gist of it.

Many thanks.

You have a link to the dialogue? or can you tell us about at what point in the film this dialogue occurs?

The dialogue is the last 2 lines at the end of the scene in the Balboa Coffee shop where Noriko and Hattori discuss wedding presents @ 34'30" into the film.

OK, the literal translation is correct. But the meaning has to do with jealousy.

When you make pickled radish (takuan) you cut the radish into slices before pickling. Sometimes the skin is so hard, the knife doesn't completely cut through the skin, and some slices get stuck together. So the radish slices are connected. This is a metaphor for a jealous person being hung up on some other person (being stuck to that other person like a connected radish slice). The jealous person is said to have a dull knife because he/she can't make a clean break from that other person.

So I'm not entirely sure about the dialogue because I haven't seen the whole movie, but Hattori must have had some other girlfriend or love interest. So when he invites Noriko to the concert, Noriko is suspicious because she thinks he must have bought the tickets with that other girl in mind. So she quizzes him, "Are you sure you bought these for me?". He tries to reassure her, but she guesses he really bought them with that other girl in mind, and so she declines the offer. Hattori sighs and gives up, and that's when he throws out the "connected radish" comment. He's saying, "your're radishes are still connected, aren't they?" (meaning, your still hung up on that other person). And she kind of laughs it off playfully and says, "yeah, my knife is still dull", half-joking, but I guess maybe half-true?

Anyway, it seems to be a kind of obscure phrase, maybe used around Kyoto mostly? I can see some Japanese people commenting on this on other websites, so it must be not instantly intuitive for modern Japanese.

Majestic, thank you for the insightful and detailed reply. That has answered my question perfectly and the scene now makes sense. Hattori is engaged to another woman which explains the jealousy angle. Whether or not she is actually jealous is another matter...