A Hybrid Binary–Ternary Encoding Strategy for High-Capacity and Robust Phase Unwrapping in Fringe Projection Profilometry

Imagine trying to take a perfect 3D photo of a bumpy, shiny, or dark object without ever touching it. Scientists use a clever trick called "fringe projection profilometry" to do this. They project a series of striped patterns (like a barcode made of light) onto an object and use a camera to watch how those stripes bend and warp. By measuring the warping, a computer can calculate the object's shape. However, there's a catch: the computer only sees the stripes as a repeating loop, like a clock that resets every 12 hours. It knows the time is "3 o'clock," but it doesn't know if it's 3 AM, 3 PM, or 3 days later. To fix this, the computer needs to "unwrap" the phase, figuring out exactly which loop of the stripe pattern it is looking at. This is called "phase unwrapping." If the computer guesses the wrong loop, the 3D model gets scrambled, with parts of the object appearing in the wrong place or looking like a glitchy video game. Getting this right is crucial for everything from scanning faces for security to designing car parts, but it's notoriously difficult when there's noise, bad lighting, or if the object is very complex.

Enter a new strategy from researchers at Xi'an Technological University, who have devised a "hybrid" way to solve this puzzle. Instead of relying on just one type of code to tell the computer which loop it's on, they mixed two different coding languages together: a simple "binary" code (like a light switch that is either on or off) and a "ternary" code (a three-way switch that can be low, medium, or high). Think of it like trying to find a specific house in a giant city. A binary code is like asking, "Is the house on the left or right side of the street?" A ternary code is like asking, "Is the house on the first, second, or third block?" By combining these questions, the researchers can pinpoint the location much faster and more accurately than using just one type of question.

The paper proposes a method that uses a specific sequence of light patterns: four steps to get a high-precision "map" of the surface, three steps to get a helper map, and three special "ternary Gray code" patterns to act as the address labels. The clever part is how they read these labels. Instead of needing extra "calibration" photos (like taking a picture of a blank wall to know what "white" looks like), their system looks at the brightness of the stripes themselves to figure out the thresholds for decoding. It's like a detective who doesn't need a reference photo to know what a suspect looks like; they just analyze the clues right in front of them. This allows them to handle tricky situations where the lighting changes or the surface is shiny.

To make sure they don't make mistakes at the edges where the codes switch (the "boundary" regions), the team added a "pre-correction" step. They check if the direction of the stripes matches the logic of the address code. If the math doesn't add up—like if the address says "Block 3" but the stripes suggest "Block 2"—the system automatically swaps the address for a better candidate before finalizing the 3D shape.

The researchers tested this idea in two ways. First, they ran computer simulations with different levels of "noise" (simulating a messy, grainy image). They found that even when the image was very noisy, their method made far fewer mistakes than older techniques. Specifically, they reported that their approach reduced the overall error in counting the fringe loops by about 21 times and made the final 3D shape much smoother, reducing the root-mean-square error by about 43 times compared to uncorrected methods. In their real-world experiments, they successfully scanned complex objects like human faces and multiple items at once, proving the system works even on curved, detailed surfaces.

However, the paper also notes a limitation: the system is sensitive to "defocus," which happens if the projector isn't focused perfectly. When the light patterns get too blurry, the three-level (ternary) codes become hard to distinguish, and the error rate jumps up significantly. The researchers suggest that while their method is a robust solution for high-speed, high-precision measurements, it still struggles when the optical system is significantly out of focus. Overall, the study suggests that this hybrid binary-ternary strategy offers a powerful balance between speed, accuracy, and the ability to handle complex shapes, provided the equipment is kept in good focus.