text: The number of leaves a plant has is one of the key traits (phenotypes) describing its development and growth. Here, we propose an automated, deep learning based approach for counting leaves in model rosette plants. While state-of-the-art results on leaf counting with deep learning methods have recently been reported, they obtain the count as a result of leaf segmentation and thus require per-leaf (instance) segmentation to train the models (a rather strong annotation). Instead, our method treats leaf counting as a direct regression problem and thus only requires as annotation the total leaf count per plant. We argue that combining different datasets when training a deep neural network is beneficial and improves the results of the proposed approach. We evaluate our method on the CVPPP 2017 Leaf Counting Challenge dataset, which contains images of Arabidopsis and tobacco plants. Experimental results show that the proposed method significantly outperforms the winner of the previous CVPPP challenge, improving the results by a minimum of 50 on each of the test datasets, and can achieve this performance without knowing the experimental origin of the data (i.e. in the wild setting of the challenge). We also compare the counting accuracy of our model with that of per leaf segmentation algorithms, achieving a 20 decrease in mean absolute difference in count (|DiC|).
  @cite_0: 
  @cite_7: Following [Lempitsky and Zisserman, 2010], we seek to count objects by integrating over an object density map that is predicted from an input image. In contrast to that work, we propose to estimate the object density map by averaging over structured, namely patch-wise, predictions. Using an ensemble of randomized regression trees that use dense features as input, we obtain results that are of similar quality, at a fraction of the training time, and with low implementation effort. An open source implementation will be provided in the framework of http: ilastik.org.
  @cite_6: Our objective is to count (and localize) object instances in an image interactively. We target the regime where individual object detectors do not work reliably due to crowding, or overlap, or size of the instances, and take the approach of estimating an object density.
  @cite_23: We propose a new supervised learning framework for visual object counting tasks, such as estimating the number of cells in a microscopic image or the number of humans in surveillance video frames. We focus on the practically-attractive case when the training images are annotated with dots (one dot per object). Our goal is to accurately estimate the count. However, we evade the hard task of learning to detect and localize individual object instances. Instead, we cast the problem as that of estimating an image density whose integral over any image region gives the count of objects within that region. Learning to infer such density can be formulated as a minimization of a regularized risk quadratic cost function. We introduce a new loss function, which is well-suited for such learning, and at the same time can be computed efficiently via a maximum subarray algorithm. The learning can then be posed as a convex quadratic program solvable with cutting-plane optimization. The proposed framework is very flexible as it can accept any domain-specific visual features. Once trained, our system provides accurate object counts and requires a very small time overhead over the feature extraction step, making it a good candidate for applications involving real-time processing or dealing with huge amount of visual data.
summary: Counting via density estimation. Another method to count objects in an image is by estimating their distribution, using local features. In @cite_23 , the authors have developed a loss function which aims to minimize Maximum Excess over SubArrays (MESA) distance. Other methods include density estimation by per-pixel ridge and random forest regression. Similar approaches can be found in @cite_6 @cite_0 @cite_7 , where regressors are used to infer local densities. However, these approaches are difficult to use for leaf counting, as they are challenged by the huge scale variability of leaves, as well as heavy occlusions and overlaps.