Dollar Recognizer (Multi-Stroke) — README

A lightweight, fast gesture-recognition toolkit with built in template storing that supports multi-stroke drawing. It implements three classic families of recognizers side-by-side—$1, $N, and a Penny Pincher (feature-based prefilter)—and returns uniform statistics so you can compare results, tune thresholds, and pick the best recognizer for your app or device constraints.

---

Table of Contents

• Why this project
• Algorithms at a glance
• How recognition works
• Statistics reported

---

Why this project

Gesture recognizers are often presented in isolation. This repo lets you:

• Compare $1, $N, and a feature-based prefilter (“Penny Pincher”) on the same inputs.
• See the numbers (distances, angles, confidence) that drive decisions.
• Tune thresholds to your hardware, users, and gesture set.
• Use multi-stroke gestures without being locked to stroke order or direction.

---

Algorithms at a glance

Recognizer	Multi-Stroke	Invariances	Score (intuition)	Speed	Typical Use
$1	❌ (unistroke) – used here by concatenating or pre-combining strokes when desired	Rotation, scale, translation	1 - normalized_path_distance	Very fast	Prototyping; single-stroke or pre-combined paths
$N	✅ (true multi-stroke)	Rotation, scale, translation; stroke order & direction invariance via permutations/heuristics	1 - normalized_min_distance_over_permutations	Fast–Moderate (depends on templates, permutations)	Natural multi-stroke input (e.g., characters, symbols)
Penny Pincher (Prefilter)	✅	Mostly translation/scale via normalization; coarse angle bins	Low-cost feature distance to prune template set before $N/$1	Very fast	Mobile/embedded; large template sets; early pruning

---

How recognition works

Shared preprocessing

1. Resample each stroke to a fixed number of points (e.g., 64 total; configurable).
2. Normalize: translate to centroid, scale to a reference square, optionally rotate to an indicative angle (for $1 / $N).
3. Multi-stroke handling:
   • $1: (optional) combine strokes into one path (you choose how).
   • $N: match across permutations and directions with pruning heuristics.

Matching (per recognizer)

• $1 recognizer

  • Distance metric: average path distance between candidate and template.
  • Score: $$= 1 - \frac{\text{distance}}{0.5 \cdot \sqrt{2} \cdot \text{SquareSize}}$$
  • Returns best template and stats (distance, rotation, etc.).

• $N recognizer

  • Explores stroke order/direction permutations (with pruning by start-angle/end-angle, stroke count, etc.).
  • Uses the same (or very similar) normalized distance and scoring as $1 on the best permutation.
  • Returns best template and stats, plus how many permutations were evaluated.

• Penny Pincher (feature prefilter)

  • Computes a cheap feature vector per gesture & template:
    • stroke count, total/avg stroke length, bounding-box ratio, indicative angle bin(s), start–end vector, simple direction histogram, corner count (optional), and centroid offset stats.
  • Computes a feature distance (e.g., weighted L2) and keeps top-K templates if feature_distance ≤ feature_threshold.
  • Passes survivors to $N (or $1) for exact matching.
  • Returns its own stats (feature_distance, kept/topK, reject_reason if any).

---