Abstract: Using visible‐light images，this study investigated the effects of nitrogen rate and planting density interaction on rapeseed flowering，and optimized their combination to enhance the economic and ecological value of the flowering period. A two‐factor randomized block field experiment was conducted with five nitrogen gradients（0，90，180，270，360 kg/ha）and four planting density gradients（300 000，525 000，750 000，975 000 plants/ha）. UAV digital images were used to establish the flower pixel area index（FPAI） dynamic equation for flowering process，and nitrogen‐density combinations were optimized with cumulative FPAI during full bloom（M_S2）and input cost as core indicators.Results showed that FPAI was significantly positively correlated with single‐plant flower quantity（R²=0.941 2—0.984 0）.Compared with no‐nitrogen control（N₀），nitrogen treatments（N 90—360 kg/ha）advanced the start of initial bloom（B_x），full bloom（F_x）and peak bloom（T_x） by 2.5，1.9 and 1.0 d，and extended initial bloom（S₁），full bloom（S₂）and theoretical flowering duration（S₁₊₂） by 0.6，1.5 and 2.1 d，respectively.Planting density had no significant effect on key flowering time points［F_x，T_x，E_x （the start of final bloom）］；increased density shortened S₁ and S₁₊₂ by 1.5 d and 1.0 d on average，but extended S₂ by 0.5 d.At fixed density，key flower quantity indicators all increased first and then decreased with rising nitrogen rate.The average values of theoretical maximum flowering accumulation（A），M_S2 and mean full‐bloom FPAI（MAve） under N 90—360 kg/ha treatments increased by 50.1%，64.7% and 48.1% compared with no nitrogen application treatment. When nitrogen application rate reached 360 kg/ha，increasing planting density would instead reduce flower yield.Cost optimization showed that combinations in optimized zone Ⅰ achieved the lowest input cost for target flower quantity. The optimal combinations were 580 000—780 000 plants/ha with N 157.7—195.9 kg/ha for high flower quantity，M_S2=197.2—203.1，cost 1 201.8—1 515.8 yuan/ha）；479 000—580 000 plants/ha with N 92.0—157.7 kg/ha for medium flower quantity，M_S2=176.5—197.2，cost 801.2—1 201.8 yuan/ha；438 000—479 000 plants/ha with N 55.4—92.0 kg/ha for low flower quantity，M_S2=155.7—176.5，cost 589.1—801.2 yuan/ha.Sub‐optimal combinations outside zone Ⅰ could reduce cost by 2.1%—16.0% via density‐increasing &nitrogen‐reducing or nitrogen‐increasing & density‐reducing strategies. In conclusion，FPAI is an effective indicator for monitoring rapeseed flowering dynamics. Rational nitrogen‐density synergy can increase flower quantity and regulate flowering process，with nitrogen rate playing a dominant role.The optimization zoning provides targeted nitrogen‐density configuration schemes，and offers decision support for cost‐saving and efficiency‐enhancing production of flower‐use rapeseed.

Key words: Oilseed rape, Flowering traits, Unmanned aerial vehicle, Digital image‐based detection, Flower quantity isoline, Nitrogen‐density interaction

摘要： 通过可见光图像探究施氮量与种植密度互作对油菜开花过程的影响，优化施氮量与密度组合以提升油菜花期经济和生态价值。试验采用二因素随机区组设计，设置施氮量梯度（0、90、180、270、360 kg/hm^²）和密度梯度（30.0万、52.5万、75.0万、97.5万株/hm^²），利用无人机获取油菜花期数字图像信息，构建开花过程的花像素面积指数（FPAI）动态方程，以盛花期开花累计量（M_S2）和投入成本为核心优化油菜氮密组合。结果表明，FPAI与单株开花量呈显著正相关(R^²=0.941 2~0.984 0）。与不施氮（N₀）处理相比，施氮处理（90~360 kg/hm^²）可使油菜始花期、盛花期和FPAI峰值出现时刻（B_x、F_x、T_x）分别提前2.5、1.9、1.0 d，始花期、盛花期和理论花期（S₁、S₂、S₁₊₂）分别延长0.6、1.5、2.1 d；密度对花期关键时刻［F_x、T_x、E_x（终花期开始时刻）］的影响不明显，但增密可使S₁和S₁₊₂分别缩短1.5、1.0 d，S2增加0.5 d。密度一定时，关键时刻花量（B_y、F_y、T_y、E_y）、理论最大开花累计量（A）、盛花期FPAI累计量（M_S2）及盛花期平均FPAI（M_Ave）均随施氮量增加呈先增后减的趋势；施氮处理（90~360 kg/hm^²）的主要花量指标（A、M_S2、MAve）平均值较不施氮处理分别增加50.1%、64.7%、48.1%，但施氮量达360 kg/hm^²时，增密反而会导致花量下降。基于目标花量的成本优化结果显示，优化区（Ⅰ区）氮密组合可实现氮密投入成本最低。高花量（M_S2=197.2~203.1）的最优组合为密度58.0万~78.0万株/hm^²、施氮量157.7~195.9 kg/hm^²，成本1 201.8~1 515.8 元/hm²；中花量（M_S2=176.5~197.2）的最优组合为密度47.9万~58.0万株/hm^²、施氮量92.0~157.7 kg/hm^²，成本801.2~1 201.8元/hm^²；低花量（M_S2=155.7~176.5）的最优组合为密度43.8万~47.9万株/hm^²、施氮量55.4~92.0 kg/hm^²，成本589.1~801.2元/hm^²。通过增密减氮或增氮减密策略优化氮密组合可节本2.1%~16.0%。综上所述，FPAI可作为利用数字图像监测油菜开花动态的有效指标；合理的氮密协同可提升开花量，并有效调控花期进程，施氮量在其中起主导作用。基于目标花量的成本优化分区为油菜提供了施氮量和密度配置方案，为油菜花用模式的节本增效生产提供决策支持。

关键词: 油菜, 开花性状, 无人机, 数字图像监测, 等花量线, 氮密交互