Describing Lettuce Growth Using Morphological Features Combined with Nonlinear Models

The aim of this study was to describe the sigmoidal growth behaviour of a lettuce canopy using three nonlinear models. Gompertz, Logistic and grey Verhulst growth models were established for the top projected canopy area (<i>TPCA</i>), top projected canopy perimeter (<i>TPCP</i>) and plant height (<i>PH</i>), which were measured by two machine vision views and 3D point clouds data. Satisfactory growth curve fitting was obtained using two evaluation criteria: the coefficient of determination (<i>R²</i>) and the mean absolute percentage error (<i>MAPE</i>). The grey Verhulst models produced a better fit for the growth of <i>TPCA</i> and <i>TPCP</i>, with higher <i>R²</i> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>R</mi><mrow><mi>T</mi><mi>P</mi><mi>C</mi><mi>A</mi></mrow><mn>2</mn></msubsup><mrow><mo>=</mo><mn>0.9097</mn><mo>,</mo><mo> </mo></mrow><msubsup><mi>R</mi><mrow><mi>T</mi><mi>P</mi><mi>C</mi><mi>P</mi></mrow><mn>2</mn></msubsup><mrow><mo>=</mo><mn>0.8536</mn></mrow></mrow></semantics></math></inline-formula>) and lower <i>MAPE</i> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mi>A</mi><mi>P</mi><msubsup><mi>E</mi><mrow><mi>T</mi><mi>P</mi><mi>C</mi><mi>A</mi></mrow><mrow></mrow></msubsup><mrow><mo>=</mo><mn>0.0284</mn><mo>,</mo><mo> </mo></mrow><mi>M</mi><mi>A</mi><mi>P</mi><msubsup><mi>E</mi><mrow><mi>T</mi><mi>P</mi><mi>C</mi><mi>P</mi></mrow><mrow></mrow></msubsup><mrow><mo>=</mo><mn>0.0794</mn></mrow></mrow></semantics></math></inline-formula>) values, whereas the Logistic model produced a better fit for changes in <i>PH</i> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>R</mi><mrow><mi>P</mi><mi>H</mi></mrow><mn>2</mn></msubsup><mrow><mo>=</mo><mn>0.8991</mn></mrow><mrow><mo>,</mo><mtext> </mtext></mrow><mi>M</mi><mi>A</mi><mi>P</mi><msubsup><mi>E</mi><mrow><mi>P</mi><mi>H</mi></mrow><mrow></mrow></msubsup><mrow><mo>=</mo><mn>0.0344</mn></mrow></mrow></semantics></math></inline-formula>). The maximum growth rate point and the beginning and end points of the rapid growth stage were determined by calculating the second and third derivatives of the models, permitting a more detailed description of their sigmoidal behaviour. The initial growth stage was 1–5.5 days, and the rapid growth stage lasted from 5.6 to 26.2 days. After 26.3 days, lettuce entered the senescent stage. These inflections and critical points can be used to gain a better understanding of the growth behaviour of lettuce, thereby helping researchers or agricultural extension agents to promote growth, determine the optimal harvest period and plan commercial production.