PyDenseCRF
==========

This is a (Cython-based) Python wrapper for [Philipp Krähenbühl's Fully-Connected CRFs](http://www.philkr.net/home/densecrf) (version 2).

If you use this code for your reasearch, please cite:

```
Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials
Philipp Krähenbühl and Vladlen Koltun
NIPS 2011
```

and provide a link to this repository as a footnote or a citation.

Installation
============

You can install this using `pip` by executing:

```
pip install git+https://github.com/lucasb-eyer/pydensecrf.git
```

and ignoring all the warnings coming from Eigen.

Note that you need a relatively recent version of Cython (at least version 0.22) for this wrapper,
the one shipped with Ubuntu 14.04 is too old. (Thanks to Scott Wehrwein for pointing this out.)
I suggest you use a [virtual environment](https://virtualenv.readthedocs.org/en/latest/) and install
the newest version of Cython there (`pip install cython`), but you may update the system version by

```
sudo apt-get remove cython
sudo pip install -U cython
```

Usage
=====

For images, the easiest way to use this library is using the `DenseCRF2D` class:

```python
import numpy as np
import pydensecrf.densecrf as dcrf

d = dcrf.DenseCRF2D(640, 480, 5)  # width, height, nlabels
```

Unary potential
---------------

You can then set a fixed unary potential in the following way:

```python
U = np.array(...)     # Get the unary in some way.
print(U.shape)        # -> (5, 640, 480)
print(U.dtype)        # -> dtype('float32')
U = U.reshape((5,-1)) # Needs to be flat.
d.setUnaryEnergy(U)

# Or alternatively: d.setUnary(ConstUnary(U))
```

Remember that `U` should be negative log-probabilities, so if you're using
probabilities `py`, don't forget to `U = -np.log(py)` them.

Requiring the `reshape` on the unary is an API wart that I'd like to fix, but
don't know how to without introducing an explicit dependency on numpy.

### Getting a Unary

There's two common ways of getting unary potentials:

1. From a hard labeling generated by a human or some other processing.
   This case is covered by `from pydensecrf.utils import unary_from_labels`.

2. From a probability distribution computed by, e.g. the softmax output of a
   deep network. For this, see `from pydensecrf.utils import unary_from_softmax`.

For usage of both of these, please refer to their docstrings or have a look at [the example](examples/inference.py).

Pairwise potentials
-------------------

The two-dimensional case has two utility methods for adding the most-common pairwise potentials:

```python
# This adds the color-independent term, features are the locations only.
d.addPairwiseGaussian(sxy=(3,3), compat=3, kernel=dcrf.DIAG_KERNEL, normalization=dcrf.NORMALIZE_SYMMETRIC)

# This adds the color-dependent term, i.e. features are (x,y,r,g,b).
# im is an image-array, e.g. im.dtype == np.uint8 and im.shape == (640,480,3)
d.addPairwiseBilateral(sxy=(80,80), srgb=(13,13,13), rgbim=im, compat=10, kernel=dcrf.DIAG_KERNEL, normalization=dcrf.NORMALIZE_SYMMETRIC)
```

Both of these methods have shortcuts and default-arguments such that the most
common use-case can be simplified to:

```python
d.addPairwiseGaussian(sxy=3, compat=3)
d.addPairwiseBilateral(sxy=80, srgb=13, rgbim=im, compat=10)
```

An important caveat is that `addPairwiseBilateral` only works for RGB images, i.e. three channels.
If your data is of different type than this simple but common case, you'll need to compute your
own pairwise energy using `utils.create_pairwise_bilateral`; see the [generic non-2D case](https://github.com/lucasb-eyer/pydensecrf#generic-non-2d) for details.

### Compatibilities

The `compat` argument can be any of the following:

- A number, then a `PottsCompatibility` is being used.
- A 1D array, then a `DiagonalCompatibility` is being used.
- A 2D array, then a `MatrixCompatibility` is being used.

These are label-compatibilites `µ(xi, xj)` whose parameters could possibly be [learned](https://github.com/lucasb-eyer/pydensecrf#learning). For example, they could indicate that mistaking `bird` pixels for `sky` is not as bad as mistaking `cat` for `sky`. (Wrong, old interpretation: <s>[ways to weight contributions](https://github.com/lucasb-eyer/pydensecrf/issues/8#issuecomment-188478006)</s>).

### Kernels

Possible values for the `kernel` argument are:

- `CONST_KERNEL`
- `DIAG_KERNEL` (the default)
- `FULL_KERNEL`

This specifies the kernel's precision-matrix `Λ(m)`, which could possibly be learned.
These indicate correlations between feature types, the default implying no correlation.
Again, this could possiblty be [learned](https://github.com/lucasb-eyer/pydensecrf#learning).

### Normalizations

Possible values for the `normalization` argument are:

- `NO_NORMALIZATION`
- `NORMALIZE_BEFORE`
- `NORMALIZE_AFTER`
- `NORMALIZE_SYMMETRIC` (the default)

### Kernel weight

I have so far not found a way to set the kernel weights `w(m)`.
According to the paper, `w(2)` was set to 1 and `w(1)` was cross-validated, but never specified.
Looking through Philip's code (included in [pydensecrf/densecrf](https://github.com/lucasb-eyer/pydensecrf/tree/master/pydensecrf/densecrf)),
I couldn't find such explicit weights, and my guess is they are thus hard-coded to 1.
If anyone knows otherwise, please open an issue or, better yet, a pull-request.

Inference
---------

The easiest way to do inference with 5 iterations is to simply call:

```python
Q = d.inference(5)
```

And the MAP prediction is then:

```python
map = np.argmax(Q, axis=0).reshape((640,480))
```

If you're interested in the class-probabilities `Q`, you'll notice `Q` is a
wrapped Eigen matrix. The Eigen wrappers of this project implement the buffer
interface and can be simply cast to numpy arrays like so:

```python
proba = np.array(Q)
```

Step-by-step inference
----------------------

If for some reason you want to run the inference loop manually, you can do so:

```python
Q, tmp1, tmp2 = d.startInference()
for i in range(5):
    print("KL-divergence at {}: {}".format(i, d.klDivergence(Q)))
    d.stepInference(Q, tmp1, tmp2)
```

Generic non-2D
--------------

The `DenseCRF` class can be used for generic (non-2D) dense CRFs.
Its usage is exactly the same as above, except that the 2D-specific pairwise
potentials `addPairwiseGaussian` and `addPairwiseBilateral` are missing.

Instead, you need to use the generic `addPairwiseEnergy` method like this:

```python
d = dcrf.DenseCRF(100, 5)  # npoints, nlabels

feats = np.array(...)  # Get the pairwise features from somewhere.
print(feats.shape)     # -> (7, 100) = (feature dimensionality, npoints)
print(feats.dtype)     # -> dtype('float32')

dcrf.addPairwiseEnergy(feats)
```

In addition, you can pass `compatibility`, `kernel` and `normalization`
arguments just like in the 2D gaussian and bilateral cases.

The potential will be computed as `w*exp(-0.5 * |f_i - f_j|^2)`.

### Pairwise potentials for N-D

User @markusnagel has written a couple numpy-functions generalizing the two
classic 2-D image pairwise potentials (gaussian and bilateral) to an arbitrary
number of dimensions: `create_pairwise_gaussian` and `create_pairwise_bilateral`.
You can access them as `from pydensecrf.utils import create_pairwise_gaussian`
and then have a look at their docstring to see how to use them.

Learning
--------

The learning has not been fully wrapped. If you need it, get in touch or better
yet, wrap it and submit a pull-request!

Here's a pointer for starters: issue#24. We need to wrap the gradients and getting/setting parameters.
But then, we also need to do something with these, most likely call [minimizeLBFGS from optimization.cpp](https://github.com/lucasb-eyer/pydensecrf/blob/d824b89ee3867bca3e90b9f04c448f1b41821524/pydensecrf/densecrf/src/optimization.cpp).
It should be relatively straightforward to just follow the learning examples included in the [original code](http://graphics.stanford.edu/projects/drf/densecrf_v_2_2.zip).
