CRT Object Detection

Ultralytics YOLO / Meta Detectron / Google EfficientDet. CC0.

Object detection systems use sequential feature pyramids: extract features at multiple scales through deep convolutional networks, then classify regions via learned anchor boxes. Patented: backbone architectures, feature pyramid networks, non-maximum suppression variants, anchor-free detection heads. CRT approach: every pixel value in Z/214,414,200 decomposes into 7 independent scale channels via CRT. mod 8 = coarse structure. mod 9 = medium form. mod 25 = fine edges. mod 49 = sub-pixel detail. mod 11 = integrity check. mod 13 = edge sharpness. mod 17 = contrast level. Per-channel edge detection = 7-level feature pyramid for FREE. GCD classification = O(1) object categorization. No CNN. No training. The ring IS the feature extractor.

How It Works

CRT Feature Pyramid Theorem
Image pixels encoded in Z/214,414,200 decompose into 7 CRT channels. Each channel captures features at a different scale: mod 8 (coarse) through mod 17 (contrast). Per-channel edge detection: gradient magnitude within each channel. Object boundaries = high edge energy across multiple channels. Object identity = GCD classification via gcd(pixel, N). 7 CRT channels = 7 independent feature pyramid levels. Standard FPN: sequential convolutions, patented cross-scale connections. CRT FPN: algebraic decomposition, zero cross-scale leakage (CRT independence). mod 11 = sentinel: anomalous pixels detected by mod-11 channel deviation. 3+4 split: data channels {mod 8, mod 25, mod 49} = image CONTENT (texture, detail). Parity channels {mod 9, mod 11, mod 13, mod 17} = image STRUCTURE (form, integrity, boundary, contrast). Objects = where parity channels show edges.
7-level pyramid
CRT channels
Each channel captures one scale level. No convolution. No learned weights. Algebraic.
GCD class = object class
O(1) classify
gcd(pixel, N) determines object class. No anchor boxes. No NMS. Deterministic.
mod-11 sentinel
Anomaly edges
mod-11 channel with 3x weight detects integrity violations. Same ECC property.
3+4 split
Content vs structure
Data channels = what the object looks like. Parity channels = where the object is. Natural separation.

Detection Map (Canvas)

Scene seed:

128x96 pixel detection. Left: GCD class map. Right: multi-channel edge detection (mod-11 sentinel at 3x weight). Side-by-side: content vs structure. Rendered in one cvs_blit call.

Detection Demo (Table)

Scene seed:

Synthetic 16x12 image with 3 embedded objects (mod-8-dominant, mod-9-dominant, mod-25-dominant). CRT feature pyramid decomposes into 7 scale channels. Per-channel edge detection. GCD classification colors each pixel by gcd structure.

Batch Detection

10 synthetic scenes. Per-channel edge counts. GCD class diversity per scene. CRT provides 7 independent edge maps without any convolution or learned parameters.

CRT vs Traditional Object Detection

FeaturesYOLO/Detectron: deep CNN backbone (ResNet/CSPDarknet, millions of params)CRT: 7 channel residues. No learned features. Algebraic decomposition.PyramidFPN: sequential conv + lateral connections (patented)CRT: 7 independent scales from modular arithmetic. Zero cross-scale.ClassifyAnchor boxes + NMS + confidence thresholds (patented)GCD class: gcd(pixel, N) = O(1). No anchors. No NMS. Deterministic.TrainingImageNet pretrain + COCO finetune (GPU-days)Zero training. The ring structure IS the feature extractor.ComputeGPU-bound inference (FLOPs/frame)Integer arithmetic. 7 mod operations per pixel. CPU-friendly.Patent statusUltralytics (YOLOv8), Meta (Detectron2), Google (EfficientDet, patent US10832087)CC0. Public domain. Forever.

Source code · Public domain (CC0)

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