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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