# An Image Processing Method for Measuring the Surface Area of Rapeseed Pods
## 1 Introduction  
Unlike many other crops, the primary photosynthetic organs of rapeseed include branches, stems, and pods in addition to the leaves [1]. Once the plants enter the flowering stage, the pods rapidly proliferate. The surface area of pods reaches its maximum and tends to become constant after approximately 25 days of flowering. Simultaneously, the leaves wither gradually and their area decreases sharply; therefore, the pods gradually overtake the role of leaves as the primary photosynthetic organ in rape [1]. As an essential source of photosynthesis, pods function as the \"source\" [1; 2; 3] and \"sink\" for grain formation, significantly influencing the yield and quality of rape grain [4; 5; 6; 7; 8]. The surface area of rapeseed pods is an important index widely used to measure the photosynthetic capacity of pods. It is generally believed that cultivars that produce large pods with substantial surface areas are more efficient at photosynthesis and produce larger amounts of grain. Rape pods are irregularly shaped, with varying lengths and quantities of long-bead chains. Thus, measuring the surface area of rape pods is difficult [9]. The surface area of rape pods refers to the measured surface area of the functional part of the pods. The measurement of pod surface area can be divided into two dimensions: the single-pod surface area and the multi-pod surface area (Figure 1). These areas will be referred to as \"single-pod measurement\" and \"multi-pod measurement\", with the formerserving as the basis of the latter. Currently, the methods for single pod measurement are relatively well-established and include the Clark formula [10], Leng formula [9; 11], flattening scanning [12; 13], and quasi-cylinder side area methods [14]. The Clark and Leng formula methods have a similar principle of estimating the unknown pod surface area by establishing a regression equation between the pod length/width and the actual surface area. The principle and operation of these two methods are relatively simple and widely used [15; 16; 17; 18; 19; 20; 21]. The results of these methods are obtained indirectly through mathematical models; thus, the \"actual area\" of the pods used for their correlation analysis might not be accurate owing to the limitations of the measurement techniques and conditions at that time, i.e., the measurements may not be highly accurate. Flattening scanning obtains the area value by directly measuring the flattened pod peel. These results are more accurate than the two methods described earlier as the pod peel is directly measured. However, owing to the complex operation and inefficient measurements that result from these models, they are only used to measure the \"actual area\" when there are few pods [22]. In addition, it is difficult to completely flatten the pod peels because of the shape of their chain beads; this results in a measured value that is theoretically less than the \"actual area\". The quasi-cylinder and the quasi-cone side area methods treat the pod as an approximate cylinder or cone. The pod length and average width are measured and inserted into the formula to calculate the cylinder or cone side area to obtain the measured value [23]. Although the operation of these methods is relatively simple, they exhibit calculation errors because the pods are not actually standard cylinders or cones. In the past, the common method used to measure the surface area of rapeseed pods based on the dimensions of a single pod was inaccurate, primarily because there was no method at that time that could directly measure the surface area of irregularly shaped pods. Therefore, approximate measurement results were obtained by calculating these parameters based on formulas or flattening the skin shape. The measurement of the surface area of irregularly shaped objects became accurate when three-dimensional (3-D) measurement technology became commonplace; 3-D laser technology was recognized as one of the most favorable methods for the highly accurate measurements of objects [24].