# mrcal C API

## Table of Contents

The C API consists of several headers:

`basic_geometry.h`

:*very*simple geometry structures`poseutils.h`

: pose and geometry functions`triangulation.h`

: triangulation routines`mrcal.h`

: lens models, projections, optimization

Most usages would simply `#include <mrcal.h>`

, and this would include all the
headers. This is a C (not C++) library, so X macros are used in several places
for templating.

mrcal is a research project, so the capabilities and focus are still evolving.
Thus, the interfaces, especially those in the C API are not yet stable. I do try
to maintain stability, but this is not fully impossible, especially in the
higher-level APIs (`mrcal_optimize()`

for instance). For now, assume that each
major release breaks both the API and the ABI. The migration notes for each
release are described in the relevant release notes.

The best documentation for the C interfaces is the comments in the headers. I don't want to write up anything complete and detailed until I'm sure the interfaces are stable. The available functions are broken down into categories, and described in a bit more detail here.

## Geometry structures

We have 3 structures in `basic_geometry.h`

:

`mrcal_point2_t`

: a vector containing 2 double-precision floating-point values. The elements can be accessed individually as`.x`

and`.y`

or as an array`.xy[]`

`mrcal_point3_t`

: exactly like`mrcal_point2_t`

, but 3-dimensional. A vector containing 3 double-precision floating-point values. The elements can be accessed individually as`.x`

and`.y`

and`.z`

or as an array`.xyz[]`

`mrcal_pose_t`

: an unconstrained 6-DOF pose. Contains two sub-structures:`mrcal_point3_t r`

: a Rodrigues rotation`mrcal_point3_t t`

: a translation

## Geometry functions

A number of utility functions are defined in `poseutils.h`

. Each routine has two
forms:

- A
`mrcal_..._full()`

function that supports a non-contiguous memory layout for each input and output - A convenience
`mrcal_...()`

macro that wraps`mrcal_..._full()`

, and expects contiguous data. This has many fewer arguments, and is easier to call

Each data argument (input or output) has several items in the argument list:

`double* xxx`

: a pointer to the first element in the array`int xxx_stride0`

,`int xxx_stride1`

, …: the strides, one per dimension

The strides are given in bytes, and work as expected. For a (for instance)
3-dimensional `xxx`

, the element at `xxx[i,j,k]`

would be accessible as

*(double*) &((char*)xxx)[ i*xxx_stride0 + j*xxx_stride1 + k*xxx_stride2 ]

These all have direct Python bindings. For instance `mrcal.rt_from_Rt()`

.

The `poseutils.h`

header serves as the listing of available functions.

## Triangulation

A number of triangulation routines are available in `triangulation.h`

. These
estimate the position of the 3D point that produced a given pair of
observations.

## Lens models

The lens model structures are defined here:

`mrcal_lensmodel_type_t`

: an enum decribing the lens model*type*. No configuration is stored here.`mrcal_lensmodel_t`

: a lens model type*and*the configuration parameters. The configuration lives in a`union`

supporting all the known lens models`mrcal_lensmodel_metadata_t`

: some metadata that decribes a model type. These are inherent properties of a particular model type; answers questions like: Can this model project behind the camera? Does it have an intrinsics core? Does it have gradients implemented?

The Python API describes a lens model with a string that contains the model type
and the configuration, while the C API stores the same information in a
`mrcal_lensmodel_t`

.

## Projections

The fundamental functions for projection and unprojection are defined here.
`mrcal_project()`

is the main routine that implements the "forward" direction,
and is available for every camera model. This function can return gradients in
respect to the coordinates of the point being projected and/or in respect to the
intrinsics vector.

`mrcal_unproject()`

is the reverse direction, and is implemented as a numerical
optimization to reverse the projection operation. Naturally, this is much slower
than `mrcal_project()`

. Since `mrcal_unproject()`

is implemented with a
nonlinear optimization, it has no gradient reporting. The Python
`mrcal.unproject()`

routine is higher-level, and it *does* report gradients.

The gradients of the forward `mrcal_project()`

operation are used in this
nonlinear optimization, so models that have no projection gradients defined
(CAHVORE only, as of this writing) do not support `mrcal_unproject()`

. The
Python `mrcal.unproject()`

routine still makes this work, using numerical
differences for the projection gradients.

Simple, special-case lens models have their own projection and unprojection functions defined:

void mrcal_project_pinhole(...); void mrcal_unproject_pinhole(...); void mrcal_project_stereographic(...); void mrcal_unproject_stereographic(...); void mrcal_project_lonlat(...); void mrcal_unproject_lonlat(...); void mrcal_project_latlon(...); void mrcal_unproject_latlon(...);

These functions do the same thing as the general `mrcal_project()`

and
`mrcal_unproject()`

functions, but work much faster.

## Layout of the measurement and state vectors

The optimization routine tries to minimize the 2-norm of the measurement vector \(\vec x\) by moving around the state vector \(\vec p\).

We select which parts of the optimization problem we're solving by setting bits
in the `mrcal_problem_selections_t`

structure. This defines

- Which elements of the optimization vector are locked-down, and which are given to the optimizer to adjust
- Whether we apply regularization to stabilize the solution
- Whether the chessboard should be assumed flat, or if we should optimize deformation factors

Thus the state vector may contain any of

- The lens parameters
- The geometry of the cameras
- The geometry of the observed chessboards and discrete points
- The chessboard shape

The measurement vector may contain

- The errors in observations of the chessboards
- The errors in observations of discrete points
- The penalties in the solved point positions
- The regularization terms

Given `mrcal_problem_selections_t`

and a vector \(\vec p\) or \(\vec x\), it is
useful to know where specific quantities lie inside those vectors. Here we have
4 sets of functions to answer such questions:

`int mrcal_state_index_THING()`

: Returns the index in the state vector \(\vec p\) where the contiguous block of values describing the THING begins. THING is any of- intrinsics
- extrinsics
- frames
- points
- calobject_warp

If we're not optimizing the THING, return <0

`int mrcal_num_states_THING()`

: Returns the number of values in the contiguous block in the state vector \(\vec p\) that describe the given THING. THING is any of- intrinsics
- extrinsics
- frames
- points
- calobject_warp

`int mrcal_measurement_index_THING()`

: Returns the index in the measurement vector \(\vec x\) where the contiguous block of values describing the THING begins. THING is any of- boards
- points
- regularization

`int mrcal_num_measurements_THING()`

: Returns the number of values in the contiguous block in the measurement vector \(\vec x\) that describe the given THING. THING is any of- boards
- points
- regularization

## State packing

The optimization routine works in the space of scaled parameters, and several functions are available to pack/unpack the state vector \(\vec p\):

void mrcal_pack_solver_state_vector(...); void mrcal_unpack_solver_state_vector(...);

## Optimization

The mrcal optimization routines are defined in `mrcal.h`

. There are two primary
functions, each accessing a *lot* of functionality, and taking *many* arguments:

`mrcal_optimize()`

is the entry point to the optimization routine. This function ingests the state, runs the optimization, and returns the optimal state in the same variables. The optimization routine tries out different values of the state vector by calling an optimization callback function to evaluate each one.`mrcal_optimizer_callback()`

provides access to the optimization callback function standalone,*without*being wrapped into the optimization loop

### Helper structures

We define some structures to organize the input to these functions. Each
observation has a `mrcal_camera_index_t`

to identify the observing camera:

// Used to specify which camera is making an observation. The "intrinsics" index // is used to identify a specific camera, while the "extrinsics" index is used // to locate a camera in space. If I have a camera that is moving over time, the // intrinsics index will remain the same, while the extrinsics index will change typedef struct { // indexes the intrinsics array int intrinsics; // indexes the extrinsics array. -1 means "at coordinate system reference" int extrinsics; } mrcal_camera_index_t;

When solving a vanilla calibration problem, we have a set of stationary cameras
observing a moving scene. By convention, in such a problem we set the reference
coordinate system to camera 0, so that camera has no extrinsics. So in a vanilla
calibration problem `mrcal_camera_index_t.intrinsics`

will be in \([0,
N_\mathrm{cameras})\) and `mrcal_camera_index_t.extrinsics`

will always be
`mrcal_camera_index_t.intrinsics - 1`

.

When solving a vanilla structure-from-motion problem, we have a set of moving
cameras observing a stationary scene. Here `mrcal_camera_index_t.intrinsics`

would be in \([0, N_\mathrm{cameras})\) and `mrcal_camera_index_t.extrinsics`

would be specify the camera pose, unrelated to
`mrcal_camera_index_t.intrinsics`

.

These are the limiting cases; anything in-between is allowed.

A board observation is defined by a `mrcal_observation_board_t`

:

// An observation of a calibration board. Each "observation" is ONE camera // observing a board typedef struct { // which camera is making this observation mrcal_camera_index_t icam; // indexes the "frames" array to select the pose of the calibration object // being observed int iframe; } mrcal_observation_board_t;

And an observation of a discrete point is defined by a
`mrcal_observation_point_t`

:

// An observation of a discrete point. Each "observation" is ONE camera // observing a single point in space typedef struct { // which camera is making this observation mrcal_camera_index_t icam; // indexes the "points" array to select the position of the point being // observed int i_point; // Observed pixel coordinates. This works just like elements of // observations_board_pool: // // .x, .y are the pixel observations // .z is the weight of the observation. Most of the weights are expected to // be 1.0. Less precise observations have lower weights. // .z<0 indicates that this is an outlier. This is respected on // input // // Unlike observations_board_pool, outlier rejection is NOT YET IMPLEMENTED // for points, so outlier points will NOT be found and reported on output in // .z<0 mrcal_point3_t px; } mrcal_observation_point_t;

Note that the details of the handling of discrete points may change in the future.

We have `mrcal_problem_constants_t`

to define some details of the optimization
problem. These are similar to `mrcal_problem_selections_t`

, but consist of
numerical values, rather than just bits. Currently this structure contains valid
ranges for interpretation of discrete points. These may change in the future.

// Constants used in a mrcal optimization. This is similar to // mrcal_problem_selections_t, but contains numerical values rather than just // bits typedef struct { // The minimum distance of an observed discrete point from its observing // camera. Any observation of a point below this range will be penalized to // encourage the optimizer to move the point further away from the camera double point_min_range; // The maximum distance of an observed discrete point from its observing // camera. Any observation of a point abive this range will be penalized to // encourage the optimizer to move the point closer to the camera double point_max_range; } mrcal_problem_constants_t;

The optimization function returns most of its output in the same memory as its
input variables. A few metrics that don't belong there are returned in a
separate `mrcal_stats_t`

structure:

// This structure is returned by the optimizer, and contains some statistics // about the optimization typedef struct { // generated by an X-macro /* The RMS error of the optimized fit at the optimum. Generally the residual */ /* vector x contains error values for each element of q, so N observed pixels */ /* produce 2N measurements: len(x) = 2*N. And the RMS error is */ /* sqrt( norm2(x) / N ) */ double rms_reproj_error__pixels; /* How many pixel observations were thrown out as outliers. Each pixel */ /* observation produces two measurements. Note that this INCLUDES any */ /* outliers that were passed-in at the start */ int Noutliers; } mrcal_stats_t;

This contains some statistics describing the discovered optimal solution.

## Camera model reading/writing

A simple interface for reading/writing `.cameramodel`

data from C is available:

typedef struct { double rt_cam_ref[6]; unsigned int imagersize[2]; mrcal_lensmodel_t lensmodel; double intrinsics_data[]; } mrcal_cameramodel_t; // if len>0, the string doesn't need to be 0-terminated. If len<=0, the end of // the buffer IS indicated by a 0 bytes mrcal_cameramodel_t* mrcal_read_cameramodel_string(const char* string, int len); mrcal_cameramodel_t* mrcal_read_cameramodel_file (const char* filename); void mrcal_free_cameramodel(mrcal_cameramodel_t** cameramodel); bool mrcal_write_cameramodel_file(const char* filename, const mrcal_cameramodel_t* cameramodel);

The `.cahvor`

file format is not supported