One of the ways to recognize patterns is through the intrinsic information of the object's shape by descriptors that allow us to quantitatively describe the contained shape of the object. In ichthyology, the otolith shape recognition is notable for each fish species, which allows the study of the sagitta otolith in species classification, the comparison of otolith shape across the fish ontogeny or growth, and the symmetry analysis of these structures in the case of the same fish. In the last twenty years, there has been a valuable contribution regarding otolith shape analysis and various types of morphometric descriptors have been proposed. The first objective of this work is to propose the implementation of invariant morphometric descriptors, as Discrete Compactness, Discrete Tortuosity, Non-Circularity, and Mirror-Symmetry, and compare their performance with other reported morphometric descriptors. The second objective is the implementation of the Random Forest (RF) algorithm to classify the fish species according their environment (marine, brackish, and freshwater). The right and left sagittae otoliths of 139 marine, brackish, and freshwater species (adults and juveniles) of the Yucatan peninsula and Gulf of Mexico were analysed with invariant and other reported descriptors. The global results show that the invariant descriptors can provide complementary information to other reported descriptors based on area or perimeter, given a low correlation between these features. The environment classification of species using a RF classifier showed that 83% of species correspond positively with their environment classification. This classification analysis can be a useful tool for studies of trophic dynamics, or in archaeological and paleontological studies on fossil fauna this classification tool would allow inferring from remains the environment of the studied communities and their evolution over long periods of time.

中文翻译：

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环境自动分类中来自耳石形状的不变形态描述符

识别模式的方法之一是通过描述符通过对象形状的内在信息，使我们能够定量描述对象包含的形状。在鱼类学中，每个鱼类的耳石形状识别都是显着的，这允许在物种分类中研究矢状耳石，比较整个鱼类个体发育或生长的耳石形状，以及在这种情况下这些结构的对称性分析一样的鱼。在过去的二十年中，耳石形状分析做出了宝贵的贡献，并提出了各种类型的形态测量描述符。这项工作的第一个目标是提出实现不变的形态测量描述符，如离散紧凑性、离散曲折度、非圆形和镜像对称，并将它们的性能与其他报告的形态测量描述符进行比较。第二个目标是实施随机森林 (RF) 算法，根据环境（海洋、咸水和淡水）对鱼类进行分类。对尤卡坦半岛和墨西哥湾的 139 种海洋、半咸水和淡水物种（成鱼和幼鱼）的左右矢状面耳石进行了分析，使用了不变的和其他报告的描述符。全局结果表明，如果这些特征之间的相关性较低，则不变描述符可以根据面积或周长为其他报告的描述符提供补充信息。使用 RF 分类器对物种进行环境分类显示，83% 的物种与其环境分类正对应。