Collect data materials and build datasets
(1) Construction of dairy cow target detection datasets. The datasets for this research method was derived from the video of 493 Holstein cows captured by a dairy farm camera in Baotou City, Inner Mongolia Autonomous Region in 2020. The video is 3840 segments of 45 minutes each, the video format is MPEG4, the height of the video frame is 1080 pixels, the width is 1920 pixels, the bit rate is 1639kb/s. We combined video images of dairy cows in dairy farm and in order to prevent the model training from over-fitting due to the similarity of dairy cow shapes in adjacent frames, converting the captured video into a picture by drawing one frame from eighty frames. The images that were not clear and had no dairy cows in the area to be recognized were eliminated. Finally, a total of 24210 data images were obtained after screening. Process all images through shuffling, randomly selecting 19730 as the training set, 2220 images as the validation set and 2260 images as the test set. (2) Construction of dairy cow identification datasets. Each dairy cow was cropped down and a total of 72020 dairy cow target images were obtained after screening. There were 493 cows in the images and the cow images were classified by ID. We randomly choice 293 cows as the training set with 38110 images and 200 cows as the test set with 33910 images.
The datasets of each cow in the training set and test set needed to be divided secondly. Each dairy cow was photographed at an angle of 360° and with 60° as one category, each dairy cow could be divided into six categories, representing six different angles of shooting. Finally, these 493 * 6=2958 categories of pictures were renamed.
Dairy cow target detection methods
The initial input image was resized to 640*640*3. After the backbone layer, three different scales of feature maps were generated through the head. We choice the Adam as optimizer, the initial learning rate was 0.001, the momentum factor is 0.9, the weight decay was 0.0005 and the batch size was 32. Since this paper only needed to detect the dairy cow targets, one class of dairy cow targets was needed to be classified. Before training begins, 9 anchors arranged from small to large were obtained through k-means algorithm
(Wang et al., 2022). Each ground-truth was matched with them and its width to width ratio and height to height ratio were calculated. The maximum ratio was taken and compared with the set threshold. If it was less than this threshold, it was considered a positive sample. Introducing the structure of REPVGG to improve the model performance by multi-way branching. An Aux-Head was added to work with Lead-head for model optimization. When the anchor was matched with ground-truth, three positive samples were assigned to Aux-Head and five positive samples were assigned to Lead-head with a loss weight ratio of 1:4. The final six-dimensional prediction values were obtained, which represented the border coordinates (x, y, w, h), the border confidence and the number of classes.
Cow identification methods
The Reid technique, or person Re-identification, is a sub-problem of image retrieval that uses the calculation of distance in metric learning to search for targets in an image gallery
(Hermans et al., 2017). In this paper, the target-detected images were used as the Query and we randomly selected 200 cows as the Gallery which could be representative of the entire dataset, then the images of the Query are used for the metric calculation of features with the images in the gallery to find the IDs of the target-detected dairy cows in the gallery.
Backbone
The dairy cow identification model extracted features through the improved Resnet50 network and it did not require target localization because the model was based on target detection. The high resolution feature information from the shallow network was not very useful for the recognition model, but might be used by the network as noise and affected the final recognition effect. Therefore, we only carried out feature extraction at different scales for the last two scales, setting the stride of the 1/32 scale to 1, so that the resolution of the last two scales could be kept consistent. Feature fusion refers to the fusion of feature information from different scales into a set of features through concat operation, which can better combine the features reflected by different scale features. The feature maps obtained after the last layer of convolution of the fourth scale and fifth scale were self-adaptively fused to make better use of the semantic information of the last two scale features, as shown in Fig 1.
The positive and negative sample pairs
The training method of positive and negative sample pairs seriously affects the accuracy of recognition. We set the batch size to 16 and the NUM_INSTANCE to 4, which meant randomly selecting 16 images from the prepared identity recognition datasets for processing in a mini-batch. These 16 images included 4 classes, with 4 images for each class of target. Randomly selected one from 16 images as a template sample, formed a positive sample pair with the same ID and a negative sample pair with different IDs. After data enhancement such as flip, rotation, crop, affine, calculated the distance between positive and negative samples, used the value of the maximum positive sample distance and the value of the minimum negative sample distance as hard example. Finally put it into the triplet loss for training.
Loss and distance calculation formula
This paper used a different triplet loss from the traditional Reid and proposed a joint training method with multiple loss. Center loss could reduce the intra-class gap, so adding it could reduce the gap between dairy cow features with the same ID and the same shooting angle. The data selected for the triple loss might not be uniformly distributed, which would lead to unstable performance of the model training process, slow convergence speed, easy over-fitting. We added label smoothing loss in the full connection layer, which could effectively solve the above problems, preventing the model from focusing only on the loss of correct label positions and also considering the loss of other incorrect label positions, increasing the generalization ability of the model. The triplet loss is as shown in formula (1). As described in (2) the positive and negative sample pairs, take the positive hard sample as dp and the negative hard sample as dn, set the margin to 0.25 and calculate the triplet loss. The center loss is as shown in formula (2). It simultaneously learned the deep feature center value of each cow class and reduce the distance between each cow class and its class center. The label smoothing loss is as shown in formula (3). The last layer of Resnet 50, which outputs the ID prediction logits of images, is a fully-connected layer with a hidden size being equal to numbers of cows N (N=493). Given an image, we denoted y as truth ID label and Pi as ID prediction logits of class i. The final loss is as shown in formula (4). After experimental verification, here b was 0.34.
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oeu/+neOOvXkwMQlXXNHVD1w0s+r6kjjnCFM9sb29TVRVRBO8j1mqsNmQpAbyp6xVvXv7yl3Pttddy8Bv/h3t/9JfceOON3HDDDXzn7u/xta99jZtvvpl777sX5xx79uzBarsSeqVLCLBnzx785NarqqKua7TEzLjoufht/5xDiwWP3ncam/MWpRzXXnsdj33MfiQn5vM5Wmv6YcFPnPJwQgpc/a/fTcqBN//TN/PCF/0iOWcuePlLOf/889n3iEegskzFKKGu6yIQRhNDmkrslLJxKqmwMTD6ES1QV3WJRVIslkJbSqkno6fy+azd4Iorr+JLX/oS8/mMj3/io1x00UXcdtttXHXV5bzsgl/iL374Q8477zxC6FksjnDgq18nC4SY0dZNpr5lHEegaJHWenUJVVWR8zI7cFjnSLH0YYxzXPmuK/nCFz/P1t45t9xyM69+9YV85r//N/7Vu9/Fr/zya3jOc57D5nyTb955B1/4wv+kHz19H0kJ2tkG83YTZ+uSkqaIrWbM53uotMakRFVZxjEgCJVyJSZLEbRDYbjsyiu58KJXcfbZZ/O85z+Pl11wAc97/vM49xlnc/4v/COs05z0sL0Iia5bkFLEaoMoSDEzBo+eGm3GmKPVZlGaanODA9+6E5QhKSErsGJQSggpEnPGe1+CM+cYhgWbzZzt7QX7fnIfJ52yxW+9+7LJn0e0ygxdx9bmDK0MdWWP9hiUwVQl+0By6Xcus5gMtaumuYVEbUuaKGSUrnBVQ6USrQJchc9w+hlP5OOfuJWqVpRdDa977a+SQo9oxdlnP539P/kYsiSe//M/x5133cWZT3synQ/Y2qF0RUoZZ+tV4LysW8BKfjHGrWmaxWpLBh57xt/jY7d+jKqyQCLlxOte+7rC9HFkVjc897nPZWur4YlPehJd37N10oztRcfMNDhl8OOIVhZBcO0GvU/oYWTLaVQWjNNYEUTK2UIuymRmKKX4nWv/A79z7bWIyigiGeHWT30ctODDiMqZnD0pj1TG8oef+0Ne8PPnT8oA/+a3f5sQAmeeeSYHDnwJbRxWlkMr0wCIEo2RZdlb4Ywl9v2UPQhGqSIU3TbaWiBT1ZY4aXZVV2wvDjObl/xZTlCQL2eW0rBaSgRmxzNLh2EmH7sdeobBo3MqgZwomkph0WhTA55hHNBUVLVDK0PfjXjvCdGz5Uo8IqqMuLimKeeotWGdE8Dx/Z6dzxorKCxRIpCxWiOSMVoza2fFRWWh7xPtvEGbUpGdzWdITgiaqmpXFqrrOs4551yeetbTaZUmqVLYU1LsZenF6jLeI5CnLEKp0oQTNEplIKEo37NaY51mY7OhWyw495xnMgwdIvDOSy/jDW94A49+9GmkJGWUwZjSRCswzVFMmr1c3dDTtC1N06xSxpiLr22ahqqqWEz9f+eKqZvP54xjjzHH11x3a7ItJ8GOheA9tqqnIhklCtcaV5XWe8pFiMdxRClDVdcgwjCUjOSb3zzId7/7XYZh4LOf/SxnnHEGIULl9EMo7+8OMWUUihjSRM80VqAU/aIvldIUsFYzjB3WWurakSWRJRatnQpLXdcV/64189m8pPcP0Jw8+sqO39ehrmruufceoGQg8/kcay0pCSllNjc3cc4V12gUKZUiIjlHKStLzllSShJjXK0sSb5x8OtyyqknS91aufsH3xGfOsni5Zr3/Fux1spNN90sOYvkLHLddb8rShl5+9vfLiEESSmt1vKMAklEgkgeRbKXnKSsnCXnKJKy5BQkh23xwz3S9d+X62/894I1gqnkha98lRxJWYYoMvhRRLyIeLn3nh9JtzgkItvSHfmRPPtnz5Oznnq21LWTd139bskiMkaRPooEEUmSV3idaP1VEHMqe0gQES+HD90jIl7S2MkHb7heatfIOy65VD58y8cE5eSyy6+SKCKH+oVESSIikmN5TSmt9h38uNo7ScFjB14pi0w8X8KSdymPksVLllHe+msXSzuzgkI+9KEPiohI3/dy6NARCSHJv7zkHXL39/9csojc++P7JYtIFhElx0zjHC2bT2+0IqWA955Z25QU0pbqpiBTE6lUPnPOK82GEtGvd/R2SvqyyVZclmQ7PVRK30o0qIySSAg9YiJKO7yvqNoZQ8horWiMAsnE0FNVDiWGEEZQga4bePM/+TWuu+530VbRtC3eC8YpBh+pnMHq4+dV12G30YElhJhXNR/rNEYbFtvb1HWNMY5xSDRtTdd5bFV4kUj4OLLRtqhczh+DX9UTlFIYW9zzsr+xxGJ5XUd7HjvxEUml5L/O72m+dWlVl9XNlIS4FuBWlUMpCCEdP6BwLB9K7bzU2rOUIGwZLHofp6JLaVg1TbPKg5dR7rEM3snoaXAFvd483AmmEJKTQmtbhHOMOFeqoD7EMqyiFDmXQYVSym7Y2Nig6zpSSrRtSz/0U4YhNLXF6Ac7hrY7KKUYx4DWFqMd4+BpmgbrahaLBU1bIxnqxlE5RQgjSglN7djutktvRutVYWlZgl90C6yxayKxk4+7wXI6bvleROiHvvR/6nrVwxnHUlGuKkvfj6smac7lew8wuaJRStPUTQlGtC0jf94TU2b0oTSactGYnPNUbrbFokyFo90Hdk5wtFrGGhpReRqEGcE4mmZOTlM6a4o4OQ2Vs2W4VRUrtn3kCEprFottrv+9G/nUp2/lmvf8O7yPtE1L0xiyJMZx90HYhwLGqFVPBSiXHBKSM7PZjDwVx3IuBabZrCEmj9WWrdkGIQT8WNriRchGqqqibdvdp7d2geOmzNgpSMs7MpOyKaU4fLg0T9u2LpZiGqJWOYssv7s+qbWEkI4Wf6btS3aiDT54KluvCFoKRJjKxUvpXMKJBWTpu6bAd5qRVFLO0UrIOYHKaOMIUTC2phtH6rpGTaY8+IGqskjO9H3HbD5HsoByiJQKYgiJLArtNHryZvqB/MiuOK9dxtFbWXVijVGkWNzA0HvqdpkBCf040NQNYxpRWVG7hhTiiu6lgKVpbE+m+Yl1LETkhK6kCEQ6ynNVZlycdXTdQNu2KGXw3k/1maNjHtNw+VG61wVjjUaYRtLU9LSsjajtYFpOPDDoXdzIRKAq0ljmDUzpi+SMZrI2a7MSMo1LJhRCEVYzXW5KU4l4mhG11q0GjtcHgNWxmeluA89/TVjybgllONmUwSPSqkkVBazSkEtKuczIjhsEWuJ03EG7/YEdwqH1MtPc7Q52ZjbL9w9qCPKhmrSHBEvhBiBPt3/sfKYGseVzEcpoYC5Bozq+TlL2PYa0v0MSjodj5wczshuef8twVBH+ZrDLDg+Ci8cyfld4oBnQdRSOmaJSa39fTlcfV4ha/87yuWM++/8ND8S6NbelV//K8HcFx/6vz26wnh0uF/w/QYH8mE1FBIwAAAAASUVORK5CYII=)
....(1)
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)
....(2)
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)
....(3)
![](data:image/png;base64,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)
....(4)
d
p and d
n = Feature distances of positive pair and negative pair.
a = Set to 0.25.
y
j = Label of the th image in a mini-batch.
C
yj = Denotes the th class center of deep features.
f
ti = Denotes the feature of the th image.
B = Number of batch_size.
y = Truth ID label.
P
i = Indicates ID prediction logits of class i.
A joint optimized calculation of euclidean distance and cosine similarity distance was proposed. This is because the euclidean distance measures the absolute distance between features and it is directly related to the location coordinates between the points, whereas the cosine similarity distance measures the angle of the spatial vectors and it is more concerned with the difference in direction. Because we could not determine which measurement method was most effective, we propose the combined optimization distance calculation formula. After extracting features from the target and gallery images through backbone, the results passed in xi and yi. And by combining the two distances self-adaptively, it replaced the heavy and complex traversal method to find the optimal hyper-parameter value. For example, formula (5) is the euclidean distance formula and formula (6) is the cosine similarity formula. In formula (7), represent the weight of euclidean distance and cosine distance in the joint optimization distance formula, that is the impact of the two distance formulas on the recognition effect. First initialized α, β then normalized them and put them into the network as parameter to optimize. The final printout of the weights shows that α is 0.32 and β is 0.68.
![](data:image/png;base64,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)
....(5)
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)
....(6)
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)
....(7)
d = Indicates euclidean distance between two vectors.
x
i = Represents detecting the ith dimensional feature vector of the dairy cow.
y
i = Represents the ith dimensional feature vector of the gallery dairy cow.
cosq = Cosine similarity of two vectors. Distance represents the joint optimization distance calculation formula;
a = Euclidean distance weights.
b = Cosine distance weights.
Evaluation indicator
The metrics evaluated in this experiment are the Rank-k metric and the mAP metric. Take Rank-1 as an example, it means to count whether all query images are the same as their first returned result in the gallery, which means the accuracy of the first retrieval target of the image and the same calculation can obtain Rank5 and Rank10. mAP metric means average precision mean, which is a common evaluation metric in multi-target detection and multi-label image classification. It sums and averages the average precision AP (Average Precision) in multi category tasks, that is, it represents the accuracy of all retrieval results. The calculation formula is shown in formula (8):
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGkAAAAlCAYAAABBGMctAAAY00lEQVRoge2bebxlVXXnv3vvc869971Xr6qoQkqIBiGKSEsH0dbWxG5HxAmRslHAjkZMop1EmxiVYBwYnDWaaJxtgwOxUEgUJwwICnHCASSMFvNQQNWreu/d4Zyzh1/+OOfe915VMXSK9Kc/n+59P/tz7zlnn73XXmuveV0jSexRS+23bX97RKKmQ8RSAJkAvzRM2fgykQNmxXz2Aa8rIGGpyhFTnQ6xrkkdS5LBJoNNYI3HZBmKjqiEy0AJYp2Rjxe3ULcrZwkQYAMYC8kSLQTAEchi1jzPAkIYHCkIm5l2/xFkIBbtPOO5mh3HmBFdThA4AwVgSIBt97MSC0YPHCP301ZOY9pru/Lmyu8Hcd1et0eqB7iOsIK69OQuw2UZJsvxtcfLI5PAB1IdyXIo/f3Ao6UdGNLuh8pibTNOCF+HBi5LcxoMIEOqATKcczggM+DDA+OPB4FIO09hAYthp/2bpaFLp2NPlm/WIIJCxHY8qZojjipWdacYDUp88IQAFAXKHLKJr599Dr/5kIezZsOBbBv5FTMmAJPAhAmBoh0zRGrP+tLGDCCfwBggYoCsmKaqI9gEuQghgnHYvEcKGVVVYQk4oJcZDIEl/rm3ne5hU9snP9SQxy4n1JhAO1HuwWBjZ0FEVA34+y+eyT7r1tFzPWZn19DtTZN3C4qpgtm1M1x1xZV8/GOf5bpf38zbTnsHrpM14O58oGUn0E2k33LATcM1AkzejAs+4OsaI+gUneZ948iKRgzWoxHWiU4nm8yU0nIspOXneEXbIzwtl6GYxHKJ6gC3bNwSoZoxjjG9dgZh+Tz330pf4TKDyVfz9Cc/k9W9Hmd+7tNUdclCVTEIFZu+ehY9wfe+8T2Of+Uf013f5Q//6ARWTRnMhEDtiV5GoIYYAZEw0UHMkQkkU6FkSClnsQqUCVzeI897/PDCC/nPhz2BubmSCJBGbL7qJxx80AY61tG1Bd1Oj7POvpBoISaLUiQpkFIgKYESqe2Y9ODopAQtJbLGKpCd0GRsTmjCRXa8/wdl8W7hIHqoYcNvPYb3nP4O/uBVr2Db/AjjDCUVRx35PF54xBF08oJDDn8CV1y7lW+f//0V6zew7no4DBGnMJEUMgmZZj/JQKebYS34agQp8q1zzmWq6JKv6lICKXkOPORRvPjFGznllNdRpm185lMf54wz3s9inwkXG2lygJd0YXNg9xBPjTUHrQwfywY1zwwVMAJC80grn49Pr7C79PvlqAkHWBIOXA4pcOwrj2fDuhn+6iN/iwc6dClwnPmlz7Px2BfyuCc8lvd+8D0882lPJZRhmX6xjcFj0kQsi8bas0Rk24Mmi5GZoM6ERJY8hS25+Vc/Zd/1D2FhseSugacP1FkH6OG1hgMPPAwknvzEQ5mbu5P5hWX7MS3ytCtJHoTD3CrUXUyfBslmmcJNO1l4e2zoCeoyYl1Osq3SyzLOOvsrfPAD7+dnl11LTkZ/UELyPOQ31lNWc3zuU+/DAVPdbDKVxTbIaIkUW11llDAKQEAGjCwmNe/JBKyJEEqwjk1nbeK4lx6PFAlxhKEx24fDRS644FKedcQx4C1z80PW7703q9csIaE5nGaJm1ZAtgfNtFOk1GxsuccVqwRkQIb39UT0+aBWmTVvGywxNi96H5fjnzp47o+jiiKnLiOJBEWOTJdHPfZwjnrGf+XDp/4lIUIxvRZZBwYKk7BqjC+AEAKYRmnHEEAiKRFiC6KhuUeklscYi4IwxhIIJFNiOxl33XAXRb6O2Yfuh1WNDTvoskDOIltv28x++25g1V4z3HTniNf82ak8/yUbcV2IRIy1xJBhTYE1iX65A2ssKbZY0x61qBhGkrySJB8kJUmx+Y6hluQl1ZJq1X6oNH41SaH2quug1L42KmvFJEUl+RiUFNvJ4q5Lty9F31xWfiivupk/Sd//zoVaM71aP/jRZRoqKaRFhXpOsR5IqYG1qpOUpHI0aNfwkrxqH1VJCpJULUqje5RUyivKD4PqMspLKjWQtF1+8Q6dfvJfSttraXuplx/9El1w2aXqa4ekG/XLi78imBHmocpm99E7P/wxzXmpL6lOscFN8AqSylgpKE7wIUl7TCSlUoqVytAAniTVdb00oiqlUEppKIWBqhhUhjhBcpLUHwWFFiljgvkYFFJUUrxPYqUQFUKQl7QwqjXoV1KSLr74Yr3qVa+UkjQajVTHoZJKvfjoo/T2t75NKUjRtwCoQVTwQ6lF0IRIsS/FeVXVdoVUTWCeGw0lDaVwh7ZefYn2W7dGjkxTZOrZKV34L9drqyrJb9Y5n363Tn7vZ3WnpB2SFkJfZS3FIJ3yF29XnjtdfuVP9Scn/bFsPqUf/exXqmJq9+1lW0L92+SdEiQPRGKylKkRTFmeU9YVIZbYgkbOptQ4dcZhnKUOQ8CTEnS7jrpWI2JaMeSsw5oHII1NwlpIScx0c6amM0ajPu963/s57V3vRQm6RY7FUNY1f/L61/GoRx+0tOcYQQmlRFRqRDeQJihx/MVJJ7H3qrW89eQ3EQ0MExRF0QA78vzg4kt4z4c+jJdnMJrnqI0vYGFxREEBleXb//AN1qzbhwBEPNZ5Ohng4eUvP4E3vvlkHnPIoTzu8Cfwqc98lsMf9x+IMVLFxtmeYCGl9L/dGwL1uf36K3nUwYdx2c9vmSA6KyzOBYiLbHzuM1iTzbA+X0Nu19LJV7Nmrxke+eiH8/nPf77VLYbMNRBVIRJiaB3G9qNxj0gRUnMdMYQQKEwklQuQ+px+xts47mWvZO+91ze+ijXYkOgYw01bbmXDI/Zv7tnG0Yx1jbEdinwajEd4ciB4uPmWO1gY9pmf28yN1/yKSy+7hmGC3DqC95CvY9M/XszzX/QyRqGGbI7a387Wu25pjNeR45pfXMfhhx6y5DcqEcIIm0V+8tNLOPS3f5uPfuR/8fjDn8IJLz+WylcUeUbuOqCMe+WkB8Zhjdl40fcu4PYbb+bcr5+HcVD6mppAvx6Cy/jKN89j+62/JreJT3327xj4ebbt2MZRL3oBJ554In/+hrcjQQhNzzOHsxkppWXE2X03OJwF4hBXJG647hru2nIPx73saKqywZNIvOPU0/jxjy7jzpu3sP9vHsAb3vwO3vLWd4Iz/PBH/4wxDmMNnc4UmStYM7sPc3MDrr7hBv7LM54ORcHG5z2HK6/bjMmanTuT8YbX/RnfufASbrnxJkjizC99ga995xI+/cm/wSBOfePbuen2rbzhtX/E/PaIw1CYgixPkNVcfsUvOPa/Hcv8wpADHnEgQYk871DWibJUY/bHGLW7HkJQCGG3z8ZdYSgt3KITjzlShzzpaXrkU56jrcOByjhUX5W8vFK1KA23Sndeq8fvv4/+/txvaUHSIC6oitv1sP0fqdm9HqYt9/Q1KJf001gvRQVF1UrjnoJSClIKSimp9lEpDaW0RRrerFcf/zLdduMdUpKqINWqtW20XQcefJAuveTHOvGlJ+raX92oTd+6SPOSUvSSHym1KyVVzb0glV765Je/oM9/6aPS4o0656/fqY+d+11tljRUavRx8lKUwmIpxaRBvai+RuoraqjQ2CKLUclLpaSRoubDVoXRrQqDW/WcI5+pG2+7U0979nN1x9y8ylYf9qs4wYO1aYhVRTCW2loMHqtAMo5k3IRngrEEY5uorxKWCghc+bOr+Jerf83/+P3juP4nF3Lt9dch20PJYcgwWbdx0FblLPa3MvCeABgyctvlmKOPZmFujvO+/R1cDr2OwyVhQkVmUxvGH7P3OIJmCcYRjMFmllh7qANf/uImvvilr7L/AY/C2Q6dzDDVLVg3u5Ytd95OURRc8N1/4j89/okc+h8Pa8zuWEPWmN3DUdnAnDJ8AOtg3w3r6Xa7QIe8u5oUR/QAhyH6gATRl7huB6pIkc9g6FL5PhkQkqBrMRKdJJQqpl0XZx1bt27loRv2Y9/9NnD8f385559/Pt5DTJDndqIXLbf8kve+5SRe/IpXceXtd/GsZz6Z2V6HD3z47+gHePMbT6bIHYc8/ne4dWvZKLEYwS6AGfCZs89j40tfycbfPZT912Zcdc2tzAsK67C+Bi+wFsKI7uopFkJDXmd6mGDoFh0gkTLXePUpQrXI6W86iVWmIHMFLi+wrsC5nNUzq7G2Q95dx/Nf+gqSwOUd6Kzn2Fe8jkGsGJWLxFih5PHlIqrn6c/dgeI8x/3BCbz69a/lwgt+wAUXXEqWJy7+7jfJXZc1M3szbXv0ih7rNhzAnfcMOGj/h/Hd75wP+V588byLedERT6NoD44rphtxm3fACjoOKygQs/l0k5LI2oPgEphI14DDQtbjgx/+JJvO+Tp33b3AFZdfxaYvfwVf1ZCaXNOkveeEJ2gd6Dee+FR97Nvfk3SPvvDxd8vMHKA/P+1zuvbq63TLzZu17rcO1eve9lcq+5KGfSnepHK4WY94zOG66MIfS/0bdMIRj9PTj3mVtkgaSVKKUp2kui9t+bEOeajRRzZ9S7dLSklSWemFzz9aeW8vXbdlXguSfF1KoS/N3yH57ZKGWiwXWnNUCqPGn5hrzdlBVSvFSpJUN1JKg0Fj4qdqIPkdkt8q1Xfrc5/+kDZ95cu66Ie/ULb2AF1767ZmjTQ/8bniyCtVUlVLIy8F9fX6k14tR0envv19WhgOVKmBYTiqFGNUCkt9F5WQQis+K8V6oDCaVz3cJqWhquG8qtCKN998D30jIauYVAavpCg0vEzHPfuxetLGV+gOSfK36/JL/lFk++min98jSeovzunZx5yg5x37h/KVmt1Ut+iiH/yDHvmUI3XXSFK4Tae85hix94G6oi9tD42/FCpJi9ulbT/XEzegL3/1m40Tt1jrtDedLEemFxx9nAaSdvjWZ6n70uAeKcwr1outTooajUYKdSOr55K0NTZECX7U+EySRrVUVkllWUqqpdSX/JwUtktxQXVdql9Ji2p0hC/nm0MRpdEwtL54kkKjbryiRqoax7J14kJIrdsbFZWU0r33iX+X6taRrqVUKpYLUvINkaI0qKRR0MRfXBiOWp0UZQkVBx98MFPTq9ukF6xdvYp9H/5whqMRo2rI9EwXPxoQqyEuh2o0BNPhG+edz+8+9al0u42+OHrjsTAoufCffoRzYPO8MfK7HZDoFY73nnE6+204hJlVXf76Qx/k/R/4IJvO/iIpQi+DYX8E1nLGqafRy1bT6ayiKLpY65iamWbV6lkyU7DXqn34veN/v0mAylBVnqmpWXpFweza1XS7XTJX0Mtn6OR7sWZmLbmbZfXsLDNTPVZlq+hmM8yu3oduMUPHGWanC6wzOGfJMkcv75LbnF5nhl6vi8tyMpuTZxl5Yck7OVmW3Wc3xuGco9udotObJrMF050ene4s1uasml5FJ+uyenY1a2bXkOVdMuuYnZ0hxABARmbIig7VqMkWYjOmp7pU1Yhur6DoFITQZ7qTgYVhFZmeniH0R5xz1jls3ur57HtOZzoNGp/EreOGq68ivuBJJBswqQ2UmZztZeSkN72F57/kSPYC8APIpvGAIjgHxcw04DnlXe/mlDPeCbYDpjHHE8JZRwRqgTVNaC1F6HRzhsMFIsvSIIqYNoXtRyPy3hQYS39Q0Z3uNXE928bxUgKbqF1jXnewxDqS5fmS3UKThI1q4okhBPK8c59OisWQUmgC69bi65o8bwO7pon4Lw5qpnsFUoOD5S5OuxeDjwEry2AEGEdMUFUjfD1qFrKWqhyQQknRdcQYuerKzRx26OMYzN1NWffpx5JROeTYY57HN77wCWICT4Yp8gaLzjK9ei+2l5HKwDAkyN0kMp8bcIKyrAGHZMEVYCzRB6y1OOsISkSJwtA4nLUoOg2iqhBJqcmY9kdDMI4QE+DIezPEukmpzEz3MEDulmWOCRBG41g0Iz8iKxyh9CCoyoAx4H2FNWBNRpF3MffzkYS1Gb5ugsd50ewpJZFipK48q6aXCOSDnxBoidA2o/YRR2RtD1DO/GLJzExBrwM+emTAGTG7agpDpKyGfPozZ3LCy36PqQw6sSb5DKLY+KRHk27/FZf+5GfMAwsByHNIiW33zFHM7kUABsbiTYdBXWMtZBZ8JbrdgihINidKhDrisqZCJylhDDhjGq73kC0zg5wzONtc93pT+BTJ8g4xQKqFy7sk30bWU9VYqbFhkegEnYwYagqgk/eafFLXQPJ0uhl1HbCqiWFIVcVJjkz38al9REDR7RCj2oi/xboc63I6RU7wEdMejiLLSdFjoIloNJyUc8ttW7h18/X0FwAV7Fis2HLzr7nu6l/ScTneRzqdDlde+UtGwwW2bNnCt8//Hvvutz+pGkJusLmFzHHYYw4gjEZ89OOfYD7QlFD5yOLd2wlYbrzmqhajUGPaGFjLTfk40WQbEWiKibhJcXkaI2LGosGArxt/JTOWOpRAIpFw1iHAZRabN3LM5jkoYU3COWHGKRabE7F0soLgY+uj2EYOZ1BHT15YXGHJXE6ncPjQJALvi5OKIsP72HJKo5/GLcZIipE8c5g2jx9CjXOOlBL5WNQed8RB6oLortdhv/NCfe2cc1UYlE+tEjbTl846U0e98EjZIhcWdXtGBuToaLq7Tpf++CdKqiW/oLt/fbkOXtdVB0Qxo0c89Zm6e8cObXzBEVpj0YxBMKNs+uH6+sU/V7+1sCaB6DbI7ceW19hkWxYxH1tVSnHpnTb/kSSNYxReS1H15emTpo9XqJeML0lBXkm+jby3LdUK1Q4FDZU0lFJfadhXSo2JPqpXRu+byP2uv3fXJ0CviPLv2pG/TUrzGnlp4JdmGPlalbxqP1QMteoUVaVaKfUnm0uxse1HaaRQbpPiojSYlxQ1L2lra0LKDxT681JZSV4a9Zv3Ftv3741I1U5EGj8LahEd4orsRWrXawi1EnkrMTReoZzMOx4/BmTybj2S1FeI2zQqt+iNb/xTdYueDLN6/OFP06CMqltiRKX7JcwuhHoARLK4aVIZ6TogwmjUFFq4TFgSedbBupzMWBRik8mksZhCAB/A0MEWq6lqC71ZqrqpBpoBlBLYDNcrWlMKuj2IZaBjllcNrczArixUuZfsrE27zcHbZX23bfk748pSdipNo6neSHkXonAKnPrmN/HN7/8z12+d49prrmHv2dU4CamZUMsC0uZe+m7bbuoalu8mQz1kPEqJqaLZWllF8gKSIj4aUopYk9EpupMdpNTom45tZHKK0OlMAVAUluArTO4wNmPQX2B6pgN4QuVxeYdeN9ul3K3J79uVmzGprQRdqjIaAz8+LMsRMy7X3aWcbjxuWZ5oqSgtLasksECYXKd2trkbbuZr536Nr//0Wtau6jK7z0N49GMe2eiYcQWYWUkGSbvc26Xtru5v5yGqapE5JDDOEkLCOouZFETYpjZNQBTBlhhncXSQwNdNgaKzAiJEB9agrDmdQQ06cjMCVWByYrCkrIdPDZEdgEK7XlOwOF7dtcmGZjcZkXGdZWpRmK2gwRKGVt4c42FFwHZcu42D1KzrTbOmS41FGUyFsfCnrzmRffd5GKe89Z2EAKaAOog8Myx3bSZLKjZEsiu5RLuUZN9/s9gcUsNB0QeyDKxJhAApWYIgJjW8bwzOdRCOhIheFHlDJEzrWZo4KexQaghgTWPKT7jBmMa8tWOncwyxJoAviasVJZjLtjiulEuTSrLJcO38O7FSZI5nz1bMOBa7y+fKbELy7BgannXkS4iDQNbW0igz945kY3Yh0L+1TUqyjQWXZ/hyEcbnta2Ssta0BejtvxhoSpyyXJOi9GEU0WaQykbOJ5HZxuF0gsxNIXrUtcO6Ljnt0BUESq14ay5X6qqVMkEr7uykr5Y/NMsJlJaqoSdD2nRwi+28qeJr1ESWIC7S37aNq35xKxv2OQg3k6FOzWg0pNhpTbMrYOyqT1de7wzPrvC1RV0haFJbkHe7KARy1xgGhoZJAIiNQ5lTYDBN5agaQyLLDbWAoilSFHECRROCyohY8qI7IUJ3vMsVBeM7IXty6vesSm93bxvtNMCAadEzORbOUg+H7L1mPXuvm6KqK0B0elNU9X1Ul0pjB4w9LW/MMLRF5eOWY9rQUpEtu90Wd2fLFXhmJ4jMaUI7kINzmPEkthWHgMMtC8OwE+aWKe4V95dXle+M7CV1b3Y/gF3F2TKETYwJu0wPhlad5RgsKCdF4Rg1/7NqOa/JYy3DxS57WhGEuxf4H1izu9/U0uJmp9tL98Y3bHsCl903Gbtr9w3gvZ24+zaod2va7mLz3sccK8zftEyxt2LJFKxfv4G77ryJKy6/jLzIOP/8i3jta/8n91sC8iC13WPz/6U2sQLHuiJnqcYdCJasmOFvP/E3HPWi57KtP6SsA184exMPkl1wv81I/6fOw/+lrd29TPunAjKa+vVRS7vp9r8FQ7CWSBebw2ItstzQ21k6/zu0/89Ju21LLKKQUATbyaFNpwiY6vx7k2ap/SuLP2IJdTutngAAAABJRU5ErkJggg==)
....(8)
Precisionc = Accuracy rate for a single category.
Imagesc = Number of images containing targets of this type. APK = Average accuracy for a single category.
C = Total number of categories.
There are 493 dairy cows from 6 different angles, a total of 2958 categories.
Model lightweight methods
In this paper, the iterative magnitude pruning algorithm based on lottery hypothesis was used to filter the optimal sub-network from the dairy cow identification model. The experimental steps are as follows:
- The network was initialized with pretrained weights obtained by training the Resnet50 network and the network was subjected to k times of gradient descent to obtain the weights W0 and saved, where k was 0.1%-7% of the total training times.
- Trained the dairy cow datasets and got the weight WT (1) after convergence.
- Created a mask m(1), set a fixed pruning rate and unstructuredly pruned the model W T(1).
- The weights W0, obtained by performing k-gradient descent using the original network, reset the sparse network weights obtained by pruning.
- Repeated step 2~4, pay attention to the final accuracy of each pruning model after convergence and ended pruning until the accuracy of the model begins to decline, then took the result with the highest pruning accuracy.