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Thrips are major pests affecting horticultural crops. Their effective and timely monitoring is essential for optimizing pesticide use and minimizing its environmental and economic costs. Sticky traps are commonly used to monitor thrips activity in greenhouses, but manually counting trapped thrips is labor-intensive, highlighting the necessity of a simple and time-efficient counting method. This study proposes a method for automatic counting of thrips on sticky traps from images acquired in a greenhouse using a general-purpose digital camera. This method involves two steps: extraction and classification of captured targets. In the first step, target images are automatically cropped via thresholding-based image processing. In the second step, a convolutional neural network (CNN) model is used to classify the objects in the cropped images as thrips or other objects. The CNN model was trained on trap images obtained under laboratory conditions using a scanner and trap images captured in a strawberry greenhouse using a digital camera. The counting accuracy was evaluated using images acquired from the greenhouse that were not used for training. The proposed method could count the number of thrips as accurately as or better (root mean squared error [RMSE] = 2.6 thrips, normalized RMSE [NRMSE] = 14.0%) than the widely used object-detection method YOLOv10 (RMSE = 2.7 thrips, NRMSE = 14.6%). Furthermore, its accuracy in counting thrips over time was evaluated. By training the CNN model with a dataset of trap images with high densities of thrips, the proposed method could accurately estimate the number of thrips for more than one month (RMSE = 4.6 thrips, NRMSE = 8.1%). This two-step approach enables the independent optimization of object extraction and classification processes. These results demonstrate that the proposed method is a promising tool for the effective monitoring of thrips infestations in agricultural settings.