fix: MD Backend, fixes to properly handle trailing inline text and emphasis in headers (#178)

* Small fix to properly handle trailing inline text in the md backend

Signed-off-by: Maksym Lysak <mly@zurich.ibm.com>

* Added proper handling of headers with bold, italic or emphasis

Signed-off-by: Maksym Lysak <mly@zurich.ibm.com>

* removed print

Signed-off-by: Maksym Lysak <mly@zurich.ibm.com>

* Made smarter processing of headers, with arbitrary styling

Signed-off-by: Maksym Lysak <mly@zurich.ibm.com>

* Updated docling-core to 2.2.1

Signed-off-by: Maksym Lysak <mly@zurich.ibm.com>

* Updated tests because of the change in Markdown export in docling-core

Signed-off-by: Maksym Lysak <mly@zurich.ibm.com>

---------

Signed-off-by: Maksym Lysak <mly@zurich.ibm.com>
Co-authored-by: Maksym Lysak <mly@zurich.ibm.com>

tests/data/groundtruth/docling_v2/2203.01017v2.md

@@ -139,13 +139,13 @@ tention encoding is then multiplied to the encoded image to produce a feature fo
 
 The output features for each table cell are then fed into the feed-forward network (FFN). The FFN consists of a Multi-Layer Perceptron (3 layers with ReLU activation function) that predicts the normalized coordinates for the bounding box of each table cell. Finally, the predicted bounding boxes are classified based on whether they are empty or not using a linear layer.
 
-Loss Functions. We formulate a multi-task loss Eq. 2 to train our network. The Cross-Entropy loss (denoted as l$_{s}$ ) is used to train the Structure Decoder which predicts the structure tokens. As for the Cell BBox Decoder it is trained with a combination of losses denoted as l$_{box}$ . l$_{box}$ consists of the generally used l$_{1}$ loss for object detection and the IoU loss ( l$_{iou}$ ) to be scale invariant as explained in [25]. In comparison to DETR, we do not use the Hungarian algorithm [15] to match the predicted bounding boxes with the ground-truth boxes, as we have already achieved a one-toone match through two steps: 1) Our token input sequence is naturally ordered, therefore the hidden states of the table data cells are also in order when they are provided as input to the Cell BBox Decoder , and 2) Our bounding boxes generation mechanism (see Sec. 3) ensures a one-to-one mapping between the cell content and its bounding box for all post-processed datasets.
+Loss Functions. We formulate a multi-task loss Eq. 2 to train our network. The Cross-Entropy loss (denoted as l$\_{s}$ ) is used to train the Structure Decoder which predicts the structure tokens. As for the Cell BBox Decoder it is trained with a combination of losses denoted as l$\_{box}$ . l$\_{box}$ consists of the generally used l$\_{1}$ loss for object detection and the IoU loss ( l$\_{iou}$ ) to be scale invariant as explained in [25]. In comparison to DETR, we do not use the Hungarian algorithm [15] to match the predicted bounding boxes with the ground-truth boxes, as we have already achieved a one-toone match through two steps: 1) Our token input sequence is naturally ordered, therefore the hidden states of the table data cells are also in order when they are provided as input to the Cell BBox Decoder , and 2) Our bounding boxes generation mechanism (see Sec. 3) ensures a one-to-one mapping between the cell content and its bounding box for all post-processed datasets.
 
 The loss used to train the TableFormer can be defined as following:
 
-l$_{box}$ = λ$_{iou}$l$_{iou}$ + λ$_{l}$$_{1}$ l = λl$_{s}$ + (1 - λ ) l$_{box}$ (1)
+l$\_{box}$ = λ$\_{iou}$l$\_{iou}$ + λ$\_{l}$$\_{1}$ l = λl$\_{s}$ + (1 - λ ) l$\_{box}$ (1)
 
-where λ ∈ [0, 1], and λ$_{iou}$, λ$_{l}$$_{1}$ ∈$_{R}$ are hyper-parameters.
+where λ ∈ [0, 1], and λ$\_{iou}$, λ$\_{l}$$\_{1}$ ∈$\_{R}$ are hyper-parameters.
 
 ## 5. Experimental Results
 
@@ -175,9 +175,9 @@ We also share our baseline results on the challenging SynthTabNet dataset. Throu
 
 The Tree-Edit-Distance-Based Similarity (TEDS) metric was introduced in [37]. It represents the prediction, and ground-truth as a tree structure of HTML tags. This similarity is calculated as:
 
-TEDS ( T$_{a}$, T$_{b}$ ) = 1 - EditDist ( T$_{a}$, T$_{b}$ ) max ( | T$_{a}$ | , | T$_{b}$ | ) (3)
+TEDS ( T$\_{a}$, T$\_{b}$ ) = 1 - EditDist ( T$\_{a}$, T$\_{b}$ ) max ( | T$\_{a}$ | , | T$\_{b}$ | ) (3)
 
-where T$_{a}$ and T$_{b}$ represent tables in tree structure HTML format. EditDist denotes the tree-edit distance, and | T | represents the number of nodes in T .
+where T$\_{a}$ and T$\_{b}$ represent tables in tree structure HTML format. EditDist denotes the tree-edit distance, and | T | represents the number of nodes in T .
 
 ## 5.4. Quantitative Analysis
 
@@ -376,9 +376,9 @@ Here is a step-by-step description of the prediction postprocessing:
 - 3.a. If all IOU scores in a column are below the threshold, discard all predictions (structure and bounding boxes) for that column.
 - 4. Find the best-fitting content alignment for the predicted cells with good IOU per each column. The alignment of the column can be identified by the following formula:
 
-alignment = arg min c { D$_{c}$ } D$_{c}$ = max { x$_{c}$ } - min { x$_{c}$ } (4)
+alignment = arg min c { D$\_{c}$ } D$\_{c}$ = max { x$\_{c}$ } - min { x$\_{c}$ } (4)
 
-where c is one of { left, centroid, right } and x$_{c}$ is the xcoordinate for the corresponding point.
+where c is one of { left, centroid, right } and x$\_{c}$ is the xcoordinate for the corresponding point.
 
 - 5. Use the alignment computed in step 4, to compute the median x -coordinate for all table columns and the me-