How Tall Was the Suspect at the Doorway?
A gas-station doorway camera is mounted 3.1 m above the floor with a 15° downward tilt and a 2.8 mm wide-angle lens, recording 640×480 at 15 fps. The door frame is known to be 80.0 inches high at the threshold. In the best frame, the frame spans 160 pixels vertically and the suspect-walking through the doorway-spans 165 pixels. The suspect's feet are approximately 0.4 m closer to the camera than the door plane; the camera is 4.4 m from the door plane. The floor is level, but the suspect wears work boots and a baseball cap, and is captured mid-stride with a slight forward lean. A detective asks for a height estimate to compare with a 6'2" (74 in) person of interest. The image is H.264 at low bitrate and shows ringing around high-contrast edges.
1. List the error sources and explain how each biases the height estimate.
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Perspective is the largest bias: the suspect is closer to the camera than the door, so he projects larger; a naive ratio overestimates height. Wide-angle lens distortion compresses or stretches edges, so measuring near the frame border adds error. Pixel measurement uncertainty of ±1 px on a 160 px reference is about ±0.6%, or ±0.5 in. The suspect's forward lean and mid-stride posture reduce apparent stature, while work boots add roughly 1 in and the cap adds to the head outline. Compression ringing blurs the crown and sole edges. The assumed 80.0-inch door height may differ from as-built dimensions. The camera tilt means vertical measurements are not a simple planar ratio. Any one of these can shift the result by inches, which matters when comparing to a 74-inch person.
2. Describe a defensible measurement method and calculate a range.
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Start with the naive ratio: 165/160 × 80.0 = 82.5 in. Correct for distance using the pinhole approximation, where apparent size scales as 1/distance: multiply by 4.0/4.4 = 0.909, giving 75.0 in. This assumes the whole body is at the closer plane; the head is slightly farther than the feet, so treat it as an approximation. A vanishing-point or homography check on the door plane and a camera calibration model would refine the result. Add about 1 in for boots, subtract for the lean, and propagate ±1 px on each measurement, lens distortion, and reference uncertainty. A defensible report gives a range such as 74–78 in (188–198 cm), not a point estimate. The 74-inch person falls inside the range, so the measurement neither includes nor excludes him.
3. What wording would you use in the report so the estimate is not overstated?
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State the measurement basis: camera height, tilt, lens, door reference, pixel spans, assumed distances, and the correction applied. Then write: 'The suspect's stature is estimated at 74–78 inches (188–198 cm). This range reflects pixel measurement, perspective correction, lens distortion, posture, and footwear uncertainty. It does not identify any individual and should not be used alone to include or exclude a person of interest.' Include the original frame, the measurement annotations, and the calculation so another examiner can reproduce it. Avoid phrases like 'matches the suspect' or 'is 6 feet 3 inches'; those imply precision the data do not support. If the comparison is critical, recommend a controlled scene measurement or a calibrated 3D reconstruction.