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Estimating accurate and reliable fruit and vegetable counts from images in real-world settings, such as orchards, is a challenging problem that has received significant recent attention. Estimating fruit counts before harvest provides useful information for logistics planning. While considerable progress has been made toward fruit detection, estimating the actual counts remains challenging. In practice, fruits are often clustered together. Therefore, methods that only detect fruits fail to offer general solutions to estimate accurate fruit counts. Furthermore, in horticultural studies, rather than a single yield estimate, finer information such as the distribution of the number of apples per cluster is desirable. In this work, we formulate fruit counting from images as a multi-class classification problem and solve it by training a Convolutional Neural Network. We first evaluate the per-image accuracy of our method and compare it with a state-of-the-art method based on Gaussian Mixture Models over four test datasets. Even though the parameters of the Gaussian Mixture Model-based method are specifically tuned for each dataset, our network outperforms it in three out of four datasets with a maximum of 94\% accuracy. Next, we use the method to estimate the yield for two datasets for which we have ground truth. Our method achieved 96-97\% accuracies. For additional details please see our video here: https://www.youtube.com/watch?v=Le0mb5P-SYc}{https://www.youtube.com/watch?v=Le0mb5P-SYc.