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论文范文
1. Introduction Chinese yam (Dioscorea opposita) is one of the most exported crops from Japan. The value of yam exports reached 1.89 billion JPY in 2013 [1]. About 90% of the total yield of yam in Japan was produced in two prefectures, Hokkaido (45.8%) and Aomori (44.0%), in 2012 [2]. In both prefectures, mechanical cultivation is used for rapid expansion of production. However, seed yams (seed tubers of yams), which are uniformly cutoff yams (Figure 1), are manually produced and require the effort of 300 people·h/ha. In order to reduce the cost of production and improve the yield of yams, mechanization for producing seed yams is required. The problem in the mechanization of seed yam production is how to determine the cutoff positions for each yam. It is expected that a yam be uniformly cut with a desired weight and without much loss. Therefore, under the assumption of equal density among yams, it is required that the shape of the yam be measured, since the weight of each seed yam can be calculated using the shape and the cutoff positions. A straightforward way to measure the shape of a yam is to scan a yam using sensors. However, this includes three problems: () cost of the sensor, () speed of the process, and () accuracy of the scanning (e.g., trichomes of a yam can reduce the accuracy of the scanning). Another way is to use images of yams for shape determination. Such an approach has been widely used in fruit/crop grading, classification and removal before shipment [3–6]. Computational and statistical methodologies have been provided [7–16]. In the case of producing seed yams, the problem is much simpler than the general problem mentioned above for fruits and crops; we can assume a regular pattern of yams (see Figure 1) and do not have to strictly check yam damage, because the purpose here is to know the shape of yams quickly without the use of many devices (i.e., a low-cost way). In this paper, we propose a Bayesian framework to address issues () and (), that is, to provide a low-cost and high-speed way for shape prediction of yam. Our hypothesis is that shape of yam can be predicted by a few key diameters at fixed positions, under an assumption that shape of yam can be represented by a set of diameters. In order to examine this hypothesis, we need to construct a model that gives a relationship between the diameters to be predicted and the key diameters, which can be measured. A difficulty in the model construction is that measurements of diameters for each sample are insufficient and unsteady. Thus, we introduce a Bayesian framework to relieve such difficulty. Bayesian method is a technique for statistical inference that updates the probability based on a prior probability for random parameters in a model based on observations. By using Bayesian inference, we can set up a prior distribution for parameters based on prior information, which is available in advance, to obtain robust estimates for parameters for lack of observations, so Bayesian method is especially useful when observational data are insufficient for estimation. In this reason, methods of Bayesian data analysis are widely applied (e.g., [17]). Bayesian inference is particularly important in time series analysis. For example, [18] proposed an approach of Bayesian smoothness priors for analyzing time varying structure in a dynamic system; it is useful for a case that there are some missing data in time series. In this paper, we apply the technique of smoothness priors to the problem of shape prediction of Chinese yam. The proposed method estimates the whole shape of a yam based on a few measurements of the key diameter of the yam. The two issues regarding the measurement of the shape of yams are overcome by using the proposed method, since the diameter of a yam are easily and accurately measured without any sensors. We estimated optimal positions of the diameter to be measured by minimizing the error of the shape prediction. We also illustrated high performance of the proposed method in terms of estimating the shape of yams using a sample data set, which contains the length, weight, and diameters at intervals of 10 to 50 mm (Figure 2, see also Section 2.2) of 111 yams from Hokkaido, Japan. After the construction of the proposed method using the sample data set, the method gives whole shape prediction of yam based on a few key diameters without any scanners or images of yam. 
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