The title of the book,Applications of topology and geometry in computer vision,is based on two tools: persistent homology, a powerful algebraic topological approach;The second is bionic pattern recognition theory,which is a geometric covering method. This book focuses on the theoretical basis of the reference book,mainly to introduce the persistent homology and bionic patterr recognition theory in the application of computer vision.In the selection of materials in this book,we do not design difficult theories and do not go to the pointwhen it comes to more in-depth theory or application,we will qive references,interested readers can reac for themselves.The content arrangement follows the following principles:(1) persistent homology involves more basic knowledge such as abstract algebra,category,algebraic topology,etc.We extracted the necessary preparatory knowledge and condensed it into two chapters. This is beneficial for beainners.can help them accurately lock the necessarv information. take a lot less detours.(2) With the previous preliminary knowledge,we will systematically introduce the persistent homology theory, mainly including the construction of complex and the calculation of homology group,which are the core content of the persistent homology theory.(3) The theory is connected with practice,and several typical applications of persistent homology are introduced appropriately.