## 1 Introduction  
Agriculture is the foundation of social stability and national development in many countries, especially in developing countries. Adequate supply of grain and other basic agricultural products is an irreplaceable foundation for ensuring sufficient stability of market prices. Meanwhile, food security is a crucial support for national economic security. Therefore, it is a particularly urgent and meaningful task to strengthen the macro-control of the food market and ensure food security and market stability at present. Rice plays an essential role in agricultural production as the most significant food crop [1]. With the rapid increase in the population, the country's demand for food is also growing. We have problems with declining soil quality and eutrophication [2]. Since rice plays a key role in food security, it is necessary to study the growth status of rice. Industrialization reduces the arable land area, so it is required to increase the yield of rice in order to increase the total yield of rice. Therefore, rice growth and cultivation of high-yield varieties has become a major research issue in agricultural research institutions [3]. The study of rice growth is very critical to political, economic and social stability. Due to the development of computer information technology, image-processing technology is becoming more and more advanced. In order to detect and extract data from the overall growth state of rice, phenotypic feature data extraction from rice image has been widely used. Compared with artificial experiments, this method can reduce subjective errors and improve the accuracy of data. The main content of image processing is to cut the areas in the original image that need to be studied, and then extract the features of specific areas according to color components and texture features [4]. Fractal geometry has a self-similar character. When the geometries with fractal characteristics are magnified at different multiples, the observed properties are similar and have a fractal dimension in space [5; 6]. The concept of fractals was first put forward by [PERSON] in 1973. He defined a fractal as a set, which expresses the symmetry or self-similarity of the whole and the part in a certain sense. There are many fractal phenomena in nature, such as coastlines, lightning, human lungs, material surfaces, etc., which can be approximately regarded as fractal sets [7]. However, the typical fractal sets are specially constructed by mathematicians, so they have a standard and strict self-similarity. However, in nature, most of the objects we study do not have strict self-similarity characteristics, but only meet statistical self-similarity. Therefore, in research, we mainly carry out approximate processing on the objects to explore the quasi-self-similarity [8]. The dimension of fractal geometry is usually not an integer dimension, so the integer dimension used in the traditional Euclidean space cannot describe the fractal shape. [PERSON] proposed the concept of a non-integer dimension or fractal dimension [9]. The fractal dimension describes a complex ratio that reflects how the details of the pattern change with the scale of the measurement [10]. It is used in all areas of science because it provides a measure of the complexity and irregularity of a given object [11]. Complexity is a change in detail and scale. As the fractal dimension increases, the complexity of the object also increases. As a long-neglected part of geometry, fractals can help us to study nature from a new perspective and find order in apparent disorder [12]. Since the 1970s, the application of fractal theory has developed rapidly and gradually become an important new subject. Fractals have been widely used in natural and social sciences such as biology, chemistry, physics, material science, computer graphics, seismology, economics and so on. It is now one of the frontier research disciplines of many disciplines all over the world [13].