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If a CNN is trained on images focusing on an object, will it also recognize when multiple such objects are present in the image?

For example can a network trained on single flower images also identify image having many such flowers in a bunch?

Is the answer same if situation is reversed? That is, can a CNN trained on bunch of flower images also identify single flower image?

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This question greatly depends on the pixel-space scale of the objects, but if the scale of the objects is similar and enough data are provided to curb overfitting, then yes, it should work both ways.

The Caveats: A Neural Network is merely a glorified (hierarchical) Template Matcher. If the visual appearance of multiple objects in an image is strongly correlated with the learned template, those objects will each get a high response from that convolutional kernel. Convolutional templates can achieve some degree of scale-invariance through stacking multiple layers and using a downsampling strategy such as Max Pooling, but virtually all convolutional neural networks are practically quite limited as to the scale of features that they will respond to. As a simple example, a neural network consisting of two convolutional layers of 3x3 spatial kernels each with padding of 1 separated by a 2x2 Max Pooling downsampling layer would have a receptive field of at most 8x8 pixels per output location (3x2+2), where the last 3 is the last layer's kernel width, the middle 2 is the downsampling factor, and the last 2 is the input padding reachable from the first kernel's output. Trying to classify any objects larger than this would result in a failure to match the learned template, so in fact CNNs are sensitive to the scale of their inputs, but due to weight sharing across spatial locations, a strong response trained from a single item should activate for multiple items of similar scale and (to some extent) vice-versa.

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