The choice of image format is important for an image processing application. It is closely linked to the domain habits of the application, and also to the use that you want to make of these images.
The most frequent formats for image processing are the PNG and JPEG formats; they can be used without fear of losing data. The PNG has a transparency feature which the JPEG does not.
As such, if you use sites like Unsplash for images the format WebP, developed by Google, is used. In your application you must use the WebP format. At the same time, if you create images for a website the WebP format is the one to use; the image upload time is quicker.
If you are developing medical software you have to use DICOM format to treat the images. The DICOM format contains digital images, but also numerous other pieces of information relating to the patient (marital status, age, weight etc) and also the exam carried out (region examined, imaging technique used, etc), date of purchase, medical practitioner etc.
If you are developing an application of multiple sizes for different screen types (tablet, phones) and your images are graphics, you need the SVG format. Here the images are remade at new sizes on different screens. Plus there is no aliasing at the front area either.
You can also develop your own personal image format which contains the pixel image data, the image width, the pixel format and the data fields personal to your application. Your images are only usable by your application.