The present disclosure relates to a class-agnostic object segmentation system that automatically detects, segments, and selects objects within digital images irrespective of object semantic classifications. For example, the object segmentation system utilizes a class-agnostic object segmentation neural network to segment each pixel in a digital image into an object mask. Further, in response to detecting a selection request of a target object, the object segmentation system utilizes a corresponding object mask to automatically select the target object within the digital image. In some implementations, the object segmentation system utilizes a class-agnostic object segmentation neural network to detect and automatically select a partial object in the digital image in response to a target object selection request.