Formulation Of A N-Degree Polynomial For Depth Estimation using a Single Image

The depth of a visible surface of a scene is the distance between the surface and the sensor. Recovering depth information from two-dimensional images of a scene is an important task in computer vision that can assist numerous applications such as object recognition, scene interpretation, obstacle avoidance, inspection and assembly. Various passive depth computation techniques have been developed for computer vision applications. They can be classified into two groups. The first group operates using just one image. The second group requires more than one image which can be acquired using either multiple cameras or a camera whose parameters and positioning can be changed. This project is aimed to find the real depth of the object from the camera which had been used to click the photograph. An n-degree polynomial was formulated, which maps the pixel depth of an image to the real depth. In order to find the coefficients of the polynomial, an experiment was carried out for a particular lens and thus, these coefficients are a unique feature of a particular camera. The procedure explained in this report is a monocular approach for estimation of depth of a scene. The idea involves mapping the Pixel Depth of the object photographed in the image with the Real Depth of the object from the camera lens with an interpolation function. In order to find the parameters of the interpolation function, a set of lines with predefined distance from camera is used, and then the distance of each line from the bottom edge of the picture (as the origin line) is calculated.

💡 Research Summary

The paper addresses the classic computer‑vision problem of recovering metric depth from a single two‑dimensional image. Rather than relying on stereo rigs, structured light, time‑of‑flight sensors, or deep‑learning models that demand large training datasets and substantial computational resources, the authors propose a purely geometric, calibration‑based approach that maps a simple image measurement—pixel depth—to real‑world distance using an N‑degree polynomial.

The methodology consists of two distinct phases. In the calibration phase, a specific camera–lens combination is fixed, and a set of planar lines (or rods) is placed at known distances from the optical centre. Each line is photographed, and the vertical distance in pixels from the line’s lower edge to the bottom edge of the image is measured; this quantity is defined as “pixel depth.” The known physical distance from the camera to the line constitutes the “real depth.” By repeating this procedure for multiple distances, a paired dataset ((p_i, D_i)) is assembled, where (p_i) is pixel depth and (D_i) is real depth.

In the modeling phase, the authors fit an N‑degree polynomial of the form

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