The form of a remote sensing index is generally empirically defined, whether by choosing specific reflectance bands, equation forms or its coefficients. These spectral indices are used as preprocessing stage before object detection/classification. But no study seems to search for the best form through function approximation in order to optimize the classification and/or segmentation. The objective of this study is to develop a method to find the optimal index, using a statistical approach by gradient descent on different forms of generic equations. From six wavebands images, five equations have been tested, namely: linear, linear ratio, polynomial, universal function approximator and dense morphological. Few techniques in signal processing and image analysis are also deployed within a deep-learning framework. Performances of standard indices and DeepIndices were evaluated using two metrics, the dice (similar to f1-score) and the mean intersection over union (mIoU) scores. The study focuses on a specific multispectral camera used in near-field acquisition of soil and vegetation surfaces. These DeepIndices are built and compared to 89 common vegetation indices using the same vegetation dataset and metrics. As an illustration the most used index for vegetation, NDVI (Normalized Difference Vegetation Indices) offers a mIoU score of 63.98% whereas our best models gives an analytic solution to reconstruct an index with a mIoU of 82.19%. This difference is significant enough to improve the segmentation and robustness of the index from various external factors, as well as the shape of detected elements.

We introduce a new dataset for goat detection that contains 6160 annotated images captured under varying environmental conditions. The dataset is intended for developing machine learning algorithms for goat detection, with applications in precision agriculture, animal welfare, behaviour analysis, and animal husbandry. The annotations were performed by expert in computer vision, ensuring high accuracy and consistency. The dataset is publicly available and can be used as a benchmark for evaluating existing algorithms. This dataset advances research in computer vision for agriculture.