From c1bc397cfb22702762778f2075739a4202463419 Mon Sep 17 00:00:00 2001 From: chokevin8 Date: Tue, 7 Nov 2023 20:26:11 +0900 Subject: [PATCH] updated CAM blog --- _posts/2023-10-20-class-activation-maps.md | 17 ++++++++++------- assets/images/hirescam.png | Bin 0 -> 580577 bytes 2 files changed, 10 insertions(+), 7 deletions(-) create mode 100644 assets/images/hirescam.png diff --git a/_posts/2023-10-20-class-activation-maps.md b/_posts/2023-10-20-class-activation-maps.md index 9ce38b2833a7..a4b4f4442ecf 100644 --- a/_posts/2023-10-20-class-activation-maps.md +++ b/_posts/2023-10-20-class-activation-maps.md @@ -90,23 +90,26 @@ to find our equation for evaluating our activation score for Grad-CAM: $$Y_c = \sum_{k} {\alpha_k}^{c} \cdot F^{k} \text{ where } {\alpha_k}^{c} = \frac{1}{Z} \sum_{i}\sum_{j} \frac{\delta Y^{c}}{\delta A_{(i,j)}^{k}} (5)$$

Equation #5 is one-step short of completion. Why? The gradients can be negative or positive! We are only interested in finding features that have a positive influence -on class $$c$$. This means that the activation score should be positive, and to have a positive gradient, the feature map should be positive as well. Negative gradients -most likely belong to features in the image that are correlated with classes that are not $$c$$. Therefore, we utilize ReLU to suppress negative gradients and keep positive gradients: +on class $$c$$. This means that the activation score should be positive, and to have a positive gradient, the feature map should be positive as well. Therefore, with Grad-CAM +we can highlight regions in the image, or features, that contribute to increasing the class activation score. On the other hand, negative gradients +most likely belong to features in the image that are correlated with classes that are not $$c$$, and therefore we apply ReLU function to suppress negative gradients and only keep positive gradients:

$$Y_c = ReLU (\sum_{k} {\alpha_k}^{c} \cdot F^{k}) \text{ where } {\alpha_k}^{c} = \frac{1}{Z} \sum_{i}\sum_{j} \frac{\delta Y^{c}}{\delta A_{(i,j)}^{k}} (6)$$

Equation #6 above is the final equation for Grad-CAM. Now, even though CAMs were widely used for classification, they could definitely also be used for semantic segmentation tasks where each pixel is labeled as a class. In this case, however, we have to modify equation #6 a bit. This is because image classification outputs a single class distribution (ex. this image is a dog), image semantic segmentation doesn't, as it outputs logits for every pixel $$(a,b)$$ predicted for class $$c$$. Therefore, it makes sense to sum all of these pixels as the activation score so that -it becomes a single class distribution like image classification. We therefore modify the $$Y^{c}$$ in the gradient to $$\sum_{(a,b) \in M}{y_{(a,b)}}^{c}$$ where $$M$$ is a set of all pixel indices that belong +it becomes a single class distribution like image classification. We therefore modify the $$Y^{c}$$ in the gradient to $$\sum_{(a,b) \in M}{Y_{(a,b)}}^{c}$$ where $$M$$ is a set of all pixel indices that belong to class $$c$$ in the segmentation prediction. The final equation for Grad-CAM in image segmentation is shown below:

-$$Y_c = ReLU (\sum_{k} {\alpha_k}^{c} \cdot F^{k}) \text{ where } {\alpha_k}^{c} = \frac{1}{Z} \sum_{i}\sum_{j} \frac{\delta Y^{c}}{\delta A_{(i,j)}^{k}} (6)$$ - +$$Y_c = ReLU (\sum_{k} {\alpha_k}^{c} \cdot F^{k}) \text{ where } {\alpha_k}^{c} = \frac{1}{Z} \sum_{i}\sum_{j} \frac{\delta \sum_{(a,b) \in M}{Y_{(a,b)}}^{c}}{\delta A_{(i,j)}^{k}} (7)$$

- -However, if we look at the equation for Grad-CAM carefully, there is a critical issue- the gradients are averaged due to global average pooling (GAP). Why can this be a problem? +However, if we look at the equation #6 or #7 above for Grad-CAM carefully, there is a critical issue- the gradients are averaged due to global average pooling (GAP). Why can this be a problem? Look at the diagram below: + +
Diagram comparing HiResCAM and GradCAM and how HiResCAM alleviates the problem of averaging the gradients in GradCAM.
+
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