H4 Planogram Compliance: A Parameter-Free, Float-Free Pipeline for Constrained Retail Vision

Planogram compliance — verifying that the right product occupies the right shelf position — is dominated by floating-point convolutional descriptors that assume GPU-class hardware. Dense IoT shelf monitoring cannot: ARM Cortex-M nodes carry no floating-point unit and no GPU. We present an end-to-end planogram pipeline that is integer-only and parameter-free. Position is encoded by the H4 transform, a lossless 40-bit integer encoding of a bounding box in eight add/subtract operations, reducing position compliance to an integer L1 threshold. Identity is resolved by retrieving a QRoPE appearance descriptor against a mined product catalogue — also integer, also with no trained weights. On the Grocery Dataset [1] (13,184 boxes, 354 images, 11 product classes) we report, with leave-one-shelf-out evaluation and 95% confidence intervals: H4 round-trip is exact on all boxes; position compliance reaches AUC 0.987, exceeding the classical IoU baseline (0.963); product identification reaches 79.7%±3.5 top-1 on a held-out shelf split, beating a parameter-free colour baseline (64.8%) and within nine points of a 2.2M-parameter zero-shot CNN (88.8%) at zero parameters; and the combined pipeline detects 100% of different-planogram violations while confirming 72.4% of compliant items, with no floating-point operation in the deployed path. Index Terms—Planogram compliance, H4 transform, Hadamard