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Patch-based image tokenization ignores the morphology of the visual world, limiting effective and efficient learning of image understanding. Inspired by subword tokenization, we introduce subobject-level adaptive token segmentation and explore several approaches, including superpixel, SAM, and a proposed Efficient and PanOptiC (EPOC) image tokenizer. Our EPOC combines boundary detection--a simple task that can be handled well by a compact model--with watershed segmentation, which inherently guarantees no pixels are left unsegmented. Intrinsic evaluations across 5 datasets demonstrate that EPOC's segmentation aligns well with human annotations of both object- and part-level visual morphology, producing more monosemantic tokens and offering substantial efficiency advantages. For extrinsic evaluation, we designed a token embedding that handles arbitrary-shaped tokens, and trained VLMs with different tokenizers on 4 datasets of object recognition and detailed captioning. The results reveal that subobject tokenization enables faster convergence and better generalization while using fewer visual tokens.