In this paper we prove results relating to two homotopy relations and four homology theories developed in the topology of digital images. We introduce a new type of homotopy relation for digitally continuous functions which we call "strong homotopy." Both digital homotopy and strong homotopy are natural digitizations of classical topological homotopy: the difference between them is analogous to the difference between digital 4-adjacency and 8-adjacency in the plane. We also consider four different digital homology theories: a simplicial homology theory by Arslan et al which is the homology of the clique complex, a singular simplicial homology theory by D. W. Lee, a cubical homology theory by Jamil and Ali, and a new kind of cubical homology for digital images with $c_1$-adjacency which is easily computed, and generalizes a construction by Karaca \& Ege. We show that the two simplicial homology theories are isomorphic to each other, but distinct from the two cubical theories. We also show that homotopic maps have the same induced homomorphisms in the cubical homology theory, and strong homotopic maps additionally have the same induced homomorphisms in the simplicial theory.

翻译：在本文中,我们证明了两个同质关系和在数字图像的地形学中开发的四种同质理论的结果。我们为数字连续功能引入了新型同质关系,我们称之为“强同质”。数字同质和强同质是古典同质的自然数字化:它们之间的差异类似于数字4对称和8对称之间的差别。我们还考虑了四种不同的数字同质理论:Arslan et 等人的简单同质理论,这是科综合体的同质理论,是D. W. Lee的单一同质理论,是Jamil和Ali的异族同质理论,是数字图像与$_1对称的新型异同质关系,这很容易计算出来,并概括了Karca ⁇ Ege 的构造。我们发现,两种简单同性同质理论是相互不同的,但与两个分立体理论不同。我们还显示,同性同性同性同性主义的同性理论是同一的,同性同性主义的同性理论是同一的。