Over-imposing 3D models over photos is troublesome, (and very approximate) as the FOV on photos was difficult to match the FOV of a 3D model without a precise mathematical formula. The attached example shows my most recent project, where we tried to overlap 3D model over an actual site photo, without trying to make it “super-photo-realistic”, but rather “eye-pleasant” using a field of view (FOV) that human eye would like to see. But what is this FOV value anyway?

What is “normal view” for the human eye?

The human eye is capable of discerning motion and limited detail over a horizontal angle in excess of 180 degrees (depending somewhat on the individual). In full-frame 35mm parlance, that would require a fisheye lens with a focal length of about 6mm; however, unlike the camera lens, the human eye, because of the shape of the retina and the processing power of the brain, automatically re-maps the image into rectilinear space. More practically, the brain analyzes an area of the overall image corresponding to an ovoid cone approximately 25-to-30 degrees in height and 35-to-45 degrees in width as what one “sees.”

Transposing this to Digital SLR camera (APS sensor size)

Nikon SRL DX format is used for this example. There is no corresponding camera lens that exactly matches what the eye perceives as “normal.” However, the so-called “normal” lenses come close. Its focal length is derived from the diagonal of the rectilinear area of its image sensor, be it film (in the case of full-frame 35mm, that would be 24x36mm) or digital (in the case of Nikon DX sensors, it is 15.6×23.7mm). Using the Pythagorean Theorem (the square of the hypotenuse of a right triangle is equal to the sum of the squares of its other two sides), for full-frame 35mm, that would be a lens with a focal length of 43.27mm, and, for DX format, it would be a lens having a focal length of 28.37mm.

With 35mm cameras, a lens with a focal length of 35mm is usually considered to be wide-angle; however, in reality, it is no more “wide-angle” than a “normal” 50mm lens is “telephoto” — each of the two is essentially equally proportionally different in opposite directions from true “normal.” It is just that the 50mm focal length is close enough and provides a pleasing enough perspective that it was adopted as a de facto standard across the industry. Regardless, with the full-frame 35mm format, almost any lens having a focal length from about 35mm to just over 60mm will give a fairly normal perspective as compared to human vision. For the Nikon DX format, this corresponds to lenses in the range of about 24mm to about 40mm.

Going Back to a 3D modeling software now…

With a Nikon SRL camera and the 18-70mm zoom lens, any focal length setting in the 28-35mm range should be really close to what a human eye sees. Considering the 1.5x crop factor of the d70 sensor, we would get to 42-52.5mm in 35mm film standard. The focal length of the lens used for site photos can be read (EXIF data) in Photoshop, and the value can be used to setup the FOV in Sketchup (or any similar 3D modeling software). Using the same camera location, both in physical and virtual world, imposing 3D model over actual site photo should be smooth and flawless.

Appendix – angular coverage for DX format focal lengths:
18 mm – H: 66.7° – V: 46.9° – D: 76.5°
24 mm – H: 52.6° – V: 36.0° – D: 61.2°
30 mm – H: 43.1° – V: 29.1° – D: 50.6°
40 mm – H: 33.0° – V: 22.1° – D: 39.1°
50 mm – H: 26.7° – V: 17.7° – D: 31.7°
60 mm – H: 22.3° – V: 14.8° – D: 26.6°
70 mm – H: 19.2° – V: 12.7° – D: 22.9°