  Deep learning self-supervised algorithms that can segment an image in a fixed
number of hard labels such as the k-means algorithm and relying only on deep
learning techniques are still lacking. Here, we introduce the k-textures
algorithm which provides self-supervised segmentation of a 4-band image
(RGB-NIR) for a $k$ number of classes. An example of its application on high
resolution Planet satellite imagery is given. Our algorithm shows that discrete
search is feasible using convolutional neural networks (CNN) and gradient
descent. The model detects $k$ hard clustering classes represented in the model
as $k$ discrete binary masks and their associated $k$ independently generated
textures, that combined are a simulation of the original image. The similarity
loss is the mean squared error between the features of the original and the
simulated image, both extracted from the penultimate convolutional block of
Keras 'imagenet' pretrained VGG-16 model and a custom feature extractor made
with Planet data. The main advances of the k-textures model are: first, the $k$
discrete binary masks are obtained inside the model using gradient descent. The
model allows for the generation of discrete binary masks using a novel method
using a hard sigmoid activation function. Second, it provides hard clustering
classes -- each pixels has only one class. Finally, in comparison to k-means,
where each pixel is considered independently, here, contextual information is
also considered and each class is not associated only to similar values in the
color channels but also to a texture. Our approach is designed to ease the
production of training samples for satellite image segmentation and the
k-textures architecture could be adapted to support different number of bands
and for more complex tasks, such as object self-segmentation. The model codes
and weights are available at https://doi.org/10.5281/zenodo.6359859
