Syntax issue on paragraph 14

README.md

@@ -11,13 +11,13 @@ In this project, we used public brain MRI data from **Alzheimers Disease Neuroim
 
 #### 2. Image preprocessing
 Image preprocessing were conducted using Statistical Parametric Mapping (SPM) software, version 12. The original MRI scans were first skull-stripped and segmented using segmentation algorithm based on 6-tissue probability mapping and then normalized to the International Consortium for Brain Mapping template of European brains using affine registration. Other configuration includes: bias, noise, and global intensity normalization. The standard preprocessing process output 3D image files with an uniform size of 121x145x121. Skull-stripping and normalization ensured the comparability between images by transforming the original brain image into a standard image space, so that same brain substructures can be aligned at same image coordinates for different participants. Diluted or enhanced intensity was used
-to compensate the structure changes. the In our project, we used both whole brain (including both grey matter and white matter) and grey matter only.
+to compensate the structure changes. In our project, we used both whole brain (including both grey matter and white matter) and grey matter only.
 
 #### 3. AlexNet and Transfer Learning
 Convolutional Neural Networks (CNN) are very similar to ordinary Neural Networks. A CNN consists of an input and an output layer, as well as multiple hidden layers. The hidden layers are either convolutional, pooling or fully connected. ConvNet architectures make the explicit assumption that the inputs are images, which allows us to encode certain properties into the architecture. These then make the forward function more efficient to implement and vastly reduce the amount of parameters in the network.
 
 #### 3.1. AlexNet
-The net contains eight layers with weights; the first five are convolutional and the remaining three are fully connected. The overall architecture is shown in Figure 1. The output of the last fully-connected layer is fed to a 1000-way softmax which produces a distribution over the 1000 class labels. AlexNet maximizes the multinomial logistic regression objective, which is equivalent to maximizing the average across training cases of the log-probability of the correct label under the prediction distribution. The kernels of the second, fourth, and fifth convolutional layers are connected only to those kernel maps in the previous layer which reside on the same GPU (as shown in Figure1). The kernels of the third convolutional layer are connected to all kernel maps in the second layer. The neurons in the fully connected layers are connected to all neurons in the previous layer. Response-normalization layers follow the first and second convolutional layers. Max-pooling layers follow both response-normalization layers as well as the fifth convolutional layer. The ReLU non-linearity is applied to the output of every convolutional and fully-connected layer. ![](images/f1.png)
+The net contains eight layers with weights; the first five are convolutional and the remaining three are fully connected. The overall architecture is shown in Figure 1. The output of the last fully-connected layer is fed to a 1000-way softmax which produces a distribution over the 1000 class labels. AlexNet maximizes the multinomial logistic regression objective, which is equivalent to maximizing the average across training cases of the log-probability of the correct label under the prediction distribution. The kernels of the second, fourth, and fifth convolutional layers are connected only to those kernel maps in the previous layer which reside on the same GPU (as shown in Figure 1). The kernels of the third convolutional layer are connected to all kernel maps in the second layer. The neurons in the fully connected layers are connected to all neurons in the previous layer. Response-normalization layers follow the first and second convolutional layers. Max-pooling layers follow both response-normalization layers as well as the fifth convolutional layer. The ReLU non-linearity is applied to the output of every convolutional and fully-connected layer. ![](images/f1.png)
 
 The first convolutional layer filters the 224x224x3 input image with 96 kernels of size 11x11x3 with a stride of 4 pixels (this is the distance between the receptive field centers of neighboring neurons in a kernel map). The second convolutional layer takes as input the (response-normalized and pooled) output of the first convolutional layer and filters it with 256 kernels of size 5x5x48. The third, fourth, and fifth convolutional layers are connected to one another without any intervening pooling or normalization layers. The third convolutional layer has 384 kernels of size 3x3x256 connected to the (normalized, pooled) outputs of the second convolutional layer. The fourth convolutional layer has 384 kernels of size 3x3x192 , and the fifth convolutional layer has 256 kernels of size 3x3x192. The fully-connected layers have 4096 neurons each.
 
@@ -51,7 +51,7 @@ In this project, we used Nibabel for MRI image processing and PyTorch Neural Net
 #### 1.1. 2D image Slice ![](images/f3.png)
 
 For inputs to 2D neural network classifier, we used 2D-image slices from a 3D MRI scans. An 3D MRI image can be viewed in three angles, perpendicular to each of three standard image coordinate axis: axial view, coronal view, and sagittal view. With observations, we identified key positions within a 3D MRI whose corresponding 2D image could present a more discernible morphology structure, in terms of the magnitude of brain atrophy, between AD cases and normal controls. (We will use the term key position referring to the position we just described) Because of the standard image space, the key position has exact same position index across different images: position index 78 for axial view; 79 for coronal view; and 57 for sagittal view Figure 3a. In the training phase, a slice index was randomly extracted at around the key positions for each of the three views, within a range of pm10 (slices). To constructed a RGB
-color image, we concatenate the key position slice, one slice one index before the key position, and one slice one index after the key position, into R, G, and B channels respectively(Figure 3b). By doing so, we hope the synthesized image could incorporate more spatial information and have some robustness.
+color image, we concatenate the key position slice, one slice one index before the key position, and one slice one index after the key position, into R, G, and B channels respectively (Figure 3b). By doing so, we hope the synthesized image could incorporate more spatial information and have some robustness.
 For validation and testing, we constructed the 2D-slice images at the exact key positions as described above for each of the three views. For each testing MRI image, three 2D-slice images (from the three views) were sequentially passed into the trained network. A final predicted label was decided by majority vote from the three 2D-slice images, that is if at least two of the three 2D images support a AD label, then the MRI scan will be predicted as "having AD".
 
 #### 1.2. Primary Structure of our AlexNet