The $1 Gesture Recognizer: Interactive Live Dashboard & Interview

1. Draw Stroke

3 templates

2. Candidate Normalization Pipeline — Drag Canvases or Sliders to Perturb

● Candidate

C

| ● Template

T_{i}

| Drag inside Steps 2–4 to see why deviating from $1 hurts recognition

Step 1: Resample N = 64

Raw: 39 → N=64 | I=6.7

Interpolates path into $N = 64$ equidistant points.

Math & Logic

I = \frac{PathLength (C)}{N - 1}

Eliminates speed variation by spacing points every distance $I$ .

Step 2: Rotate 0°

Nudge: 0° (Opt)

ω: -93.6° → 0.0°

Rotates indicative angle $ω$ to $0 °$ .

Math & Logic

ω = atan2 (p_{0 y} - \bar{y}, p_{0 x} - \bar{x})

Fast $O (N)$ angular alignment around centroid $(\bar{x}, \bar{y})$ .

Step 3: Scale

Scale X/Y: 100%/100%

129×136 → 250×250

Non-uniformly scales to ${size}^{2}$ & centers at $(0, 0)$ .

Math & Logic

q_{x} = p_{x} \frac{size}{B_{w}}, q_{y} = p_{y} \frac{size}{B_{h}}

Ensures Step 4 rotation only changes angle, not aspect ratio.

Step 4: GSS Angle

GSS Offset: 0° (Opt)

θ: -0.6° | d: 6.6

GSS finds min $d^{*}$ in $\pm 45 °$ in 10 steps.

Math & 10-Step Proof

d_{i} = \frac{1}{N} \sum_{k = 1}^{N} ∥ C_{k} - T_{i, k} ∥

score = 1 - \frac{d_{i}^{*}}{\frac{1}{2} \sqrt{2} size}

Why 10 iterations? Range $90 °$ shrinks by $φ \approx 0.618$ until $\leq 2 °$ . Since $90 ° φ^{8} = 1.92 °$ , it takes 2 initial + 8 loop evaluations = 10.

3. Live Reaction Across All Loaded Templates (Sorted by Current Score)

Overlays Template

T_{i}

, Candidate

C

, & point-to-point error lines.

The $1 Unistroke Recognizer

2. Candidate Normalization Pipeline — Drag Canvases or Sliders to Perturb

3. Live Reaction Across All Loaded Templates (Sorted by Current Score)

4. Author Interview: Understanding the Paper & Empirical Findings