I begin with a ton of quotes from the German copyright law (Urheberrecht, original, English translation):
§ 15 Allgemeines
(1) Der Urheber hat das ausschließliche Recht, sein Werk in körperlicher Form zu verwerten; das Recht umfaßt insbesondere
- das Vervielfältigungsrecht (§ 16),
- das Verbreitungsrecht (§ 17),
- das Ausstellungsrecht (§ 18).
(2) Der Urheber hat ferner das ausschließliche Recht, sein Werk in unkörperlicher Form öffentlich wiederzugeben (Recht der öffentlichen Wiedergabe). […]
Article 15 – General
(1) The author has the exclusive right to exploit his work in material form; this right shall in particular include
the right of reproduction (Article 16),
the right of distribution (Article 17),
the right of exhibition (Article 18).
(2) The author further has the exclusive right to communicate his work to the public in non-material form (right of communication to the public). […]
§ 51 Zitate
Zulässig ist die Vervielfältigung, Verbreitung und öffentliche Wiedergabe eines veröffentlichten Werkes zum Zweck des Zitats, sofern die Nutzung in ihrem Umfang durch den besonderen Zweck gerechtfertigt ist. Zulässig ist dies insbesondere, wenn
- einzelne Werke nach der Veröffentlichung in ein selbständiges wissenschaftliches Werk zur Erläuterung des Inhalts aufgenommen werden,
Article 51 – Quotations
It shall be permissible to reproduce, distribute and communicate to the public a published work for the purpose of quotation so far as such exploitation is justified to that extent by the particular purpose. This shall be permissible in particular where
- subsequent to publication individual works are included in an independent scientific work for the purpose of explaining the contents,
§ 64 Allgemeines
Das Urheberrecht erlischt siebzig Jahre nach dem Tode des Urhebers.
Article 64 – General
Copyright expires 70 years after the author’s death.
The questions relevant to your situation are:
Do you have to publish your thesis? If yes, copyright applies (§ 15) as you are reproducing and distributing the images or photographs thereof. If not, more lenient laws for private copies apply (§ 53).
Did the creators of the images die more than seventy years ago? If the images are from the 18th century or earlier, this should apply.
Did you take the photo of the image yourself? This is the most tricky question, as the photo may be a copyrightable work on its own.
Last year, a court rejected a lawsuit against Wikimedia Germany which was about using a photo of a public-domain image. The court argued that this would be an invalid prolongation of copyright that surpasses the public domain and also mentioned that a purely technical reproduction is generally not considered to be copyrightable. You can read about this here and here.
However, these links also mention lawsuits with other decisions and there is no general law about this situation.
Does § 51 (quotations) apply? – For the images, this is something that only you can decide. However, if the photograph is considered a work on its own, one may argue that you do not explain the photograph in the sense of § 51.
So, to summarise, there are several laws in your favour if you made the photographs yourself. Otherwise, you run a small risk of a copyright lawsuit, which I would consider rather low.
In general, I suggest asking the owners for their permission to be sure. Also, they may have high-quality photographs, which they can provide for you. After all, museums and similar places generally like if their exhibits are the subject of scientific works.