Wheat is widely cultivated on a global scale as a major food crop ^[1], providing the main source of calories for humans ^[2]. Similar to most gramineous plants, wheat produces tillers, which develop from axillary buds on the mother bud ^[3]. The emergence, development, and survival of tillers are very important biological characteristics of wheat ^[4]. Wheat is highly adaptable to different environments and can self-regulate population size. Tillering can have positive or negative effects on wheat yield, but reasonable tillering is positively associated with wheat yield ^[5]. Tillering of wheat is affected by external factors, and the proper application of nitrogen (N) fertilizer can significantly affect tillering and promote tillering yield ^[6]. The number of tillers also increases with an increase in planting density ^[7]. The suitable application of phosphorus fertilizer also promotes wheat tillering. It is essential to understand changes in tiller development to properly manage wheat cultivation. Currently, tiller numbers are primarily determined in manual field investigations, which are costly in terms of manpower and material resources,  and are also inefficient.

In recent years, wheat tiller numbers have been estimated using different techniques. Liu et al. ^[8] used image recognition to improve the efficiency of determining wheat populations. Tiller numbers in a wheat field were counted in pre-winter, turning green, and jointing growth stages, and canopy images of corresponding sample sections of wheat were obtained by smartphone and UAV. According to correlation analysis between canopy coverage and tiller number in the three stages, image recognition is a feasible approach to estimate tiller number in a wheat field. However, in that study, only the single element of canopy coverage was considered, and the experimental sites were all wheat fields with striped sowing. Other factors of possible influence were not thoroughly studied, and as a result, the method has low adaptability. Wu et al. ^[9] randomly selected two to three points in different test plots during the critical growth period of wheat and scanned the wheat canopy with an active multispectrometer. The mean value measured in each plot was used as the spectral value, and the corresponding range was selected to determine the tiller number in each plot. The mean value was used as the tiller number in each plot to establish models to predict the wheat tiller number, which was followed by verification. Both NDVI and RVI models successfully predicted the wheat tiller number, although the NDVI model could better detect wheat growth dynamics. However, the approach needs further validation in different ecological regions and with different wheat varieties. Shan et al. ^[10] used cameras to take vertical photos of a wheat population at the jointing stage at a fixed height, while simultaneously measuring the total tiller number within the camera frame. In analysis of photos, a threshold value of 2g-r-b factor of a color brightness value was set to separate background from wheat, and then, a 24-bit true-color image was converted to a 256-color bitmap. LoG operator was used to detect edges and extract the number of edge pixels. After training, there was no significant difference between the BP neural network fitting effect and the measured value in estimating the total stem number of wheat. Although this method is suitable for specific varieties and growth periods, wider application requires further study. Li et al. ^[11] collected wheat images using ordinary cameras. Image segmentation was used to process the wheat images. Whole wheat was extracted, and the stem part of the wheat was removed by morphological processing. The two subtractions resulted in images containing stems. After edge detection, discontinuous stalks were obtained by using Hough linear transformation. Collinear segments were connected into a line segment by filling gaps, and the number of line segments detected was used to indicate the wheat tiller number. Flowers et al. ^[12] simultaneously measured tiller density and obtained aerial images, which were all taken on cloudless days. The data set was processed to calculate the relative tiller density of each location. A relative near-infrared and relative tiller density were used to predict tiller density, and rainbow-color aerial photos successfully predicted the wheat tiller number. However, in that study, data were from wheat fields with good management of weeds, pests and diseases, and plant nutrition, which can confuse tiller density with NIR digital counts. Phillips et al. ^[13] used real-time spectral reflectance sensors to collect data in the same direction in each planted row and also measured differences between vertical and parallel movements. Reflectance measurements of bare land or natural background were collected at each site, and a corrected NDVI was calculated using the measured reflectance values. A single regression equation between tiller density and modified NDVI was derived after compensating for light interference caused by clouds, shadows, and sun angle. With the equation, optical sensors could accurately predict wheat tiller density. Yuan et al. ^[14] designed a new ALHC algorithm based on manual measurement of tiller number in two 1-m row segments and collection of ground-based lidar measurement data. The AL algorithm recognizes gaps between wheat stems and performs clustering segmentation. When tillers are too close to one another, the hierarchical algorithm cannot distinguish tillers. Therefore, to complete automatic counting of wheat tillers, the HC algorithm calculates the number of tillers in each cluster. However, this method is greatly affected by planting density. With an increase in planting density, accuracy decreases, and leaves are also wrongly identified as tillers in the clustering step. Boyle et al. ^[15] obtained RGB images of plants at 0°, 45°, and 90° through NPCC and estimated wheat tiller number by using the Frangi algorithm. Scotford et al. ^[16] estimated the wheat tiller number by combining the coefficient of variation of normalized differential vegetation index (NDVI) with the composite vegetation index measured by ultrasonic sensor height output.

In conclusion, estimating the wheat tiller number has been investigated in many previous studies, and they have contributed greatly to the optimization of models to estimate the wheat tiller number. Estimating the wheat tiller number is different from  estimating leaf area and biomass, and the same vegetation index or coverage may not be appropriate for completely different tiller states. Considering the challenges posed by the complexity of tillering in wheat, we designed a gradient vegetation feature was designed based on estimates of coverage and vegetation indices in order to improve the accuracy of tiller number estimates. We classified the  The wheat coverage and vegetation index, obtained were classified, the micro-scale variation of the wheat coverage and vegetation index were obtained, and used it it was obtained as a new variable to optimize the prediction model. Gradient characteristics were used to develop a high-precision model to estimate tiller number. With accurate estimates of tiller number, less fertilizer was applied in the place with  a higher tiller number, and more fertilizer was applied in the places with  with a lower  tiller number to promote the tiller number of wheat, so that field management could  be improved.

Tiller counts are important when  monitoring the development of many plants, especially wheat ^[15]. Most studies that estimate plant density use ground-based non-contact measurements, focusing on relatively large plants [23]^[17]. However, in crops such as wheat, with small and variable spacing between plants with narrow leaves, leaf overlap between adjacent plants and many tillers makes  visual counts difficult in the field, even when plants have more than three leaves [24]^[18]. In addition, different N treatments and planting densities significantly affect the tillering of wheat, which greatly increases the difficulty in estimating the wheat tiller number.

Yuan et al. used LiDAR to obtain data and ALHC algorithm to successfully predict wheat tiller number, but the prediction accuracy would decrease with the increase of wheat planting density ^[14]. However, the prediction model optimized by gradient features could predict wheat tiller numbers well under different planting densities, showing better adaptability compared with LiDAR. Ni et al. used the penetrability of X-ray to predict the tiller number of wheat by CT. Due to the X-ray attenuation within tillers, as all tillers can be seen in the transverse section image of the wheat culms, and the tiller number can be determined through image analysis. Nevertheless, the generation of section images  needs to scan the objects at hundreds of different angles, and the reconstruction has  a very long computation time. So, the application of CT for real-time imaging is limited due to its low speed [25]^[19]. Compared with CT, UAV can obtain images faster and more conveniently, saving a lot of time; Boyle et al. obtained RGB images of plants through NPCC and estimated wheat tiller number by using the Frangi algorithm. This method mainly estimates the tiller number of potted wheat but does not estimate the tiller number of wheat in the whole field ^[15].

3. Conclusion

Multispectral images were collected by UAV, and models were established to estimate the wheat tiller number by using data on vegetation and gradient characteristics. The primary conclusions were as follows: (1) the combination of gradient and other vegetation features improved the accuracy of wheat tiller number estimates; (2) the accuracy of the wheat tiller number estimates in models optimized by gradual vegetation features was higher than that of other models, and R² values for the three varieties were 0.7044 (P1), 0.7060 (P2), and 0.7357 (P3), it could be used to effectively estimate the wheat tiller number in a whole field and more intuitively reflected the wheat tiller number in a whole field; and (3) models optimized with gradient characteristics could better estimate the wheat tiller number under different nitrogen treatments, planting densities, and growth processe.