# projectedCuboidTo3D

## Syntax

## Description

computes the 3-D cuboid from the 2-D projected cuboid `cuboid`

= projectedCuboidTo3D(`projectedCuboid`

,`worldHeight`

,`monoCam`

)`projectedCuboid`

,
the height data of the objects contained in the projected cuboids
`worldHeight`

, and the camera parameters for the sensor that collected
the images `monoCam`

.

## Examples

### Compute 3-D Cuboids from 2-D Projected Cuboids

Specify the intrinsic parameter for a forward-facing, monocular camera sensor mounted on an ego vehicle. First, specify the focal length, the principal point of the image plane, and the output image size, in pixels.

focalLength = [309.4362 344.2161]; principalPoint = [318.9034 257.5352]; imageSize = [480 640];

Then specify the position of the camera. Position the camera 1.5 meters above the ground.

height = 1.5;

Save the intrinsic parameters as a `cameraIntrinsics`

object. Define a monocular camera sensor using the intrinsic camera parameters and the position of the camera.

camIntrinsics = cameraIntrinsics(focalLength,principalPoint,imageSize); sensor = monoCamera(camIntrinsics,height);

Define a pair of 2-D projected cuboids, specified as a 2-by-8 matrix.

projectedCuboidLabel = [302 573 255 202 376 533 255 202; 192 542 86 77 247 530 86 77];

Define the height of the objects contained within them in world units (m).

objectHeight = 1.5;

Estimate 3-D cuboids from the 2-D projected cuboids using the heights of the objects contained within them and the previously defined parameters of the monocular camera sensor.

cuboid = projectedCuboidTo3D(projectedCuboidLabel,objectHeight,sensor)

`cuboid = `*2×9*
2.3209 -1.1070 0.7500 0.5550 1.9126 1.5000 0 0 -90.0000
2.3209 0.4231 0.7500 0.4125 0.6450 1.5000 0 0 -90.0000

## Input Arguments

`projectedCuboid`

— 2-D projected cuboids

*M*-by-8 matrix

2-D projected cuboids, specified as an *M*-by-8 matrix.
*M* is the number of cuboids. Each row of the matrix defines the
front and rear rectangular faces of a 2-D projected cuboid in the form
[*x1*
*y1*
*w1*
*h1*
*x2*
*y2*,*w2*
*h2*], where [*x1*
*y1*] and [*x2*
*y2*] specify the upper-left coordinates of the front and rear
rectangular faces, and [*w1*
*h1*] and [*w2*
*h2*] specify the width and height of the corresponding faces
respectively.

`worldHeight`

— Heights of objects

real scalar | *M*-by-1 vector

Heights of objects in meters, specified as an *M*-by-1 vector or a
real scalar. *M* is the number of objects.

`monoCam`

— Camera parameters

`monoCamera`

object

Camera parameters, specified as a `monoCamera`

object. The object contains the intrinsic and extrinsic
parameters of the camera used to capture the images.

`face`

— Front face of the projected cuboids

`"rear"`

(default) | `"front"`

`"left"`

`"right"`

| *M*-by-1 string array

Front face of the projected cuboids, specified as `"rear"`

,
`"front"`

, `"left"`

, `"right"`

, or
an *M*-by-1 string array in which each element is
`"rear"`

, `"front"`

, `"left"`

, or
`"right"`

. *M* is the number of cuboids. This
argument specifies which side of each projected 2-D cuboid is aligned with the front of
the object contained within it.

`"rear"`

— Face of the 2-D projected cuboid furthest from the observer.`"front"`

— Face of the 2-D projected cuboid closest to the observer.`"left"`

— Face of the 2-D projected cuboid to the left from the perspective of the observer.`"right"`

— Face of the 2-D projected cuboid to the right from the perspective of the observer.

If you specify this argument as a scalar value, the function applies that value to
all input projected cuboids. If you specify this argument as an
*M*-by-1 string array, the function applies the value of each element
to the corresponding cuboid in `projectedCuboid`

. Use this argument
if the front of one or more detected objects is aligned with the left, right, or front
of the cuboid that contains it. For example, if a detected vehicle is facing the sensor,
specify the face value for that cuboid as `"front"`

.

**Data Types: **`char`

| `string`

## Output Arguments

`cuboid`

— 3-D cuboids

*M*-by-9 matrix

3-D cuboids, returned as an *M*-by-9 matrix. *M*
is the number of 3-D cuboids. Each row of the matrix defines the position, size, and
orientation of a 3-D cuboid in the form [*xctr*
*yctr*
*zctr*
*xlen*
*ylen*
*zlen*
*xrot*
*yrot*
*zrot*]. The function assumes `0`

degrees of roll and
pitch, and only returns the yaw angle.

Position — The center of the cuboid, in the vehicle coordinate system, is represented by

*xctr*,*yctr*,*zctr*Size — The length of the cuboid in the

*x-*,*y-*and*z-*directions is represented by*xlen*,*ylen*, and*zlen*, respectively.Orientation — The pitch, roll, and yaw angles, in degrees, are represented by

*xrot*,*yrot*,*zrot*, respectively.

This diagram shows how the function determines the yaw angle
(*zrot*) based on the angle between the face of the sensor that
detected the cuboid and the selected front face of the cuboid. In this case, the value
of `face`

is "front".

## Version History

**Introduced in R2022b**

## See Also

### Apps

### Functions

### Objects

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