VPI comes with functions that handle both polynomial and fisheye distortion models. These models are characterized by distortion coefficients and, in the case of fisheye lenses, the mapping type. The coefficients are unique for each lens and can either be supplied by the manufacturer or estimated by a lens calibration process.

What is a flat mirrorcalled

Flat glass, cover glass, flat glass has good perspective, good light transmission performance (3mm and 5mm thick colorless transparent flat glass visible light transmission ratio of 88% and 86%, respectively), high transmission rate of near red heat rays in the sun, but the visible light set indoor wall top floor and furniture, fabric and reflected far-infrared long-wave heat rays are effectively blocked. Therefore, it can produce obvious "warming effect". Colorless transparent flat glass has low ultraviolet transmittance to sunlight.

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What is a flat mirrorfor kids

Tangential distortion is defined by parameters \(p_1\) and \(p_2\) and is due to imperfect centering of the lens components and other manufacturing defects.

\begin{align*} L(\tilde{x},\tilde{y}) &= \frac{r_d}{r} \begin{bmatrix} \tilde{x} \\ \tilde{y} \end{bmatrix} \\ r_d &= M_1(\theta_d) \\ \theta_d &= \theta(1+ k_1\theta^2 + k_2\theta^4 + k_3\theta^6 + k_4\theta^8) \\ \theta &= \arctan(r) \\ r &= \sqrt{\tilde{x}^2 + \tilde{y}^2} \end{align*}

Planemirrorexamples

The Lens Distortion Correction algorithm is implemented by warping the distorted input image into a rectified, undistorted output image. It does so by performing the inverse transformation; i.e., for every pixel \((u,v)\) in the destination image, calculate the corresponding coordinate \((\check{u},\check{v})\) in the input image.

Flat mirrorreflection

Fisheye lenses can be classified depending on the relationship between the angle of incident light and where it is recorded on the image, established by the mapping function \(M_f(\theta)\).

For a complete example, consult the sample application Fisheye Distortion Correction. It implements the whole process of rectifying images captured by a fisheye lens, including the calibration process.

VPI uses the structure VPIFisheyeLensDistortionModel to store the distortion parameters, which eventually is used by the vpiWarpMapGenerateFromFisheyeLensDistortionModel to create a VPIWarpMap that undistorts the input image.

Fisheye lens is an extremely wide angle lens that produces strong barrel distortion. One of its uses is to create wide panoramas.

\begin{align*} L_r(\tilde{x},\tilde{y}) &= \frac{1+k_1r^2+k_2r^4+k_3r^6}{1+k_4r^2+k_5r^4+k_6r^6} \begin{bmatrix} \tilde{x} \\ \tilde{y} \end{bmatrix}\\ r^2 &= \tilde{x}^2 + \tilde{y}^2 \end{align*}

Polynomial distortion model, also known as Brown-Conrady model, allows representing a broad range of lens distortions, such as barrel, pincushion, mustache, etc.

For list of limitations, constraints and backends that implements the algorithm, consult reference documentation of the following functions:

Image formed by planemirror

What is a flat mirrorin physics

The equations above assume a Pinhole Camera Model. In the diagram shown in the link, the input camera is assumed to be aligned with world coordinate frame, with origin at \(O = (0,0,0)\) and optical axis colinear with world's \(Z_w\) axis. The output camera's origin is located at \(F_c\) and optical axis along \(Z_c\). Taken together, this makes the matrix \([R|t]\) transform points from input's camera space into output's.

\begin{align*} s \begin{bmatrix} \tilde{x} \\ \tilde{y} \\ 1 \end{bmatrix} &= \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \mathsf{P_{in}} \\ (x_d,y_d) &= L(\tilde{x}, \tilde{y}) \end{align*}

Planemirrorimage

\[ s \begin{bmatrix} \check{u} \\ \check{v} \\ 1 \end{bmatrix} = \mathsf{K_{in}} \begin{bmatrix} x_d \\ y_d \\ 1 \end{bmatrix} \]

\begin{align*} L_t(\tilde{x},\tilde{y}) &= \begin{bmatrix} 2p_1\tilde{x}\tilde{y} + p_2(r^2+2\tilde{x}^2) \\ p_1(r^2+2\tilde{y}^2) + 2p_2\tilde{x}\tilde{y} \end{bmatrix} \\ r^2 &= \tilde{x}^2+\tilde{y}^2 \end{align*}

VPI uses the structure VPIPolynomialLensDistortionModel to store the distortion parameters, which eventually is used by the vpiWarpMapGenerateFromPolynomialLensDistortionModel to create a VPIWarpMap that undistorts the input image.

VPI provides functions that, together with Remap algorithm, perform image rectification. The input image can have some level of distortion caused by the camera lens. The end result is an undistorted image that can optionally be reprojected into a second camera to allow, for instance, realignment of input camera's optical axis. This makes it an important stage in certain computer stereo vision applications, such as depth estimation, where two cameras must have their optical axis level and parallel.

For more information, see Lens Distortion Correction in the "C API Reference" section of VPI - Vision Programming Interface.

These equations above assume that projection is a linear operation. In reality, this is hardly the case. Lens distortions make straight lines in the real world appear projected as bent in the captured image. In order to take this into account, the distortion model is applied to the ideal, distortion-free coordinates in input camera space corresponding to the output image pixel coordinate being rendered. The resulting coordinates are the actual projected position on the input image of the rendered pixel in the output image.

What is a flat mirrorused for

The main loop of Lens Distortion Correction uses Remap, therefore performance is dominated by it. Refer to Remap's performance tables.

Flat lenses can also be called glass plates, such as prisms, reflecting lens manufacturers, Newton used it to discover the dispersion of light, but the light is from the side of the glass. If it is incident from the front, reflecting the lens, the outgoing light only increases a little offset, the outgoing light is parallel to the incident light, and can not converge or diverge, so it is not much use in optics. Flat mirrors can also realize the direction of light, for example, the secondary mirror of the Newton reflecting telescope is a flat mirror, so it is widely used. Flat lenses can also be called glass plates, flat mirrors can also achieve the direction of light, such as the Newton reflecting telescope's secondary mirror is a flat mirror, reflecting lens prices, so it is widely used. When the flat lens is ground, it is considered to be used for interferable light and will not produce stray (scratches, dents, gloss). Specifications include uncoated and coated anti-reflective multilayer lenses with visible light bands. The characteristic of the flat lens is that the focal length of the lens is the distance from the main point to the focus, and its purpose is to converge parallel light.

The distortion model is defined by a mapping function \(M_f(\theta)\) that depends on fisheye lens type, and coefficients \(k_1,k_2,k_3\) and \(k_4\) as follows: