Absolutely, there are several workable approaches for your use case—no strict camera calibration required, and they’re well-suited for low-precision, multi-camera scenarios. Here are the most practical ones tailored to your needs:

1. 单相机近似3D坐标计算（基于已知目标距离） #

Since you already have the target's distance (Z) from the camera, you can use a simplified pinhole camera model with rough approximations (no formal calibration needed):

• Core idea: Treat the camera's image center as the principal point (cx, cy)—just use the midpoint of your image resolution (e.g., for a 1920x1080 image, cx=960, cy=540).
• Approximate focal length: If you don't have the camera's exact focal length, use a reasonable estimate based on common camera types:
  • For phone/webcam cameras, the pixel focal length (fx) is typically between 1000-2000 pixels. You can refine this once by holding your marker at a known distance, measuring its pixel width, and solving fx = (marker_pixel_width * known_distance) / marker_real_width—this is a one-time quick check, not formal calibration.
• Calculation formula:

  X_3D = (X_pix - cx) * Z / fx
  Y_3D = (Y_pix - cy) * Z / fx
  

  Here, X_3D/Y_3D are the coordinates relative to the camera's optical axis (Z-axis points toward the target).

2. 多相机近似三角化（无严格外参校准） #

For multi-camera setups, you can combine the single-camera approach with rough relative positioning of your cameras:

• Step 1: Define a simple world coordinate system manually. For example, place Camera 1 at (0, 0, 0), measure the approximate distance/offset of Camera 2 relative to Camera 1 (e.g., (0.5m, 0, 0) if it's 50cm to the right) and note these rough positions.
• Step 2: For each camera, generate a 3D ray from the camera's position through the target's 2D pixel coordinate (using the single-camera formula above to get direction vectors).
• Step 3: Compute the "best fit" intersection of all rays using a least-squares method. This accounts for small errors in your rough camera positions and pixel coordinates, giving you a reasonable 3D world coordinate.
• Pro tip: Give your cameras a noticeable baseline (distance between them) rather than placing them too close—this reduces the error in the triangulated 3D position.

3. 纯比例映射（零校准参数） #

If you want to skip even the approximate focal length estimate, use the marker's known size to map pixels directly to real-world space:

• Core idea: At distance Z, the marker's real width W corresponds to w pixels in the image. Each pixel in the image then represents (W * Z) / w real-world units at that distance.
• Calculation:
  • Find the image center (centerX, centerY) as before.
  • Compute the real-world X/Y offset from the camera's optical axis:

    X_3D = (X_pix - centerX) * (W * Z) / (w * image_width)
    Y_3D = (Y_pix - centerY) * (W * Z) / (w * image_height)
    

  This is the simplest method, though it assumes your camera has no lens distortion (which is acceptable for low-precision needs).

关键注意事项 #

• The accuracy of all these methods depends heavily on the precision of your known target distance Z—if that's off, your 3D coordinates will be too.
• For multi-camera setups, avoid placing cameras with overlapping fields of view that are too narrow—wider overlap helps get a better triangulation result.
• If you need slightly better precision, you can do a one-time "quick calibration" with your marker at a few known distances to refine your focal length estimate, but this is still far less involved than formal camera calibration.

内容的提问来源于stack exchange，提问作者Nucklear