The Formula Recognition Pipeline comprises a layout detection module and a formula recognition module.
If you prioritize model accuracy, choose a model with higher accuracy. If you prioritize inference speed, select a model with faster inference. If you prioritize model size, choose a model with a smaller storage footprint.
Layout Detection Module Models:
| Model Name | Model Download Link | mAP (%) | GPU Inference Time (ms) | CPU Inference Time (ms) | Model Size (M) |
|---|---|---|---|---|---|
| RT-DETR-H_layout_17cls | Inference Model/Trained Model | 92.6 | 115.126 | 3827.25 | 470.2M |
Note: The above accuracy metrics are evaluated on PaddleX's self-built layout detection dataset, containing 10,000 images. All GPU inference times are based on an NVIDIA Tesla T4 machine with FP32 precision. CPU inference speeds are based on an Intel(R) Xeon(R) Gold 5117 CPU @ 2.00GHz with 8 threads and FP32 precision.
Formula Recognition Module Models:
| Model Name | Model Download Link | BLEU Score | Normed Edit Distance | ExpRate (%) | GPU Inference Time (ms) | CPU Inference Time (ms) | Model Size |
|---|---|---|---|---|---|---|---|
| LaTeX_OCR_rec | Inference Model/Trained Model | 0.8821 | 0.0823 | 40.01 | - | - | 89.7 M |
Note: The above accuracy metrics are measured on the LaTeX-OCR Formula Recognition Test Set. All GPU inference times are based on an NVIDIA Tesla T4 machine with FP32 precision. CPU inference speeds are based on an Intel(R) Xeon(R) Gold 5117 CPU @ 2.00GHz with 8 threads and FP32 precision.
## 2. Quick Start PaddleX supports experiencing the effects of the formula recognition pipeline through command line or Python locally. Before using the formula recognition pipeline locally, ensure you have installed the PaddleX wheel package following the [PaddleX Local Installation Guide](../../../installation/installation.en.md). ### 2.1 Experience via Command Line Experience the formula recognition pipeline with a single command, using the [test file](https://paddle-model-ecology.bj.bcebos.com/paddlex/demo_image/general_formula_recognition.png), and replace `--input` with your local path for prediction: ```bash paddlex --pipeline formula_recognition --input general_formula_recognition.png --device gpu:0 ``` Parameter Explanation: ``` --pipeline: The pipeline name, which is formula_recognition for this case. --input: The local path or URL of the input image to be processed. --device: The GPU index to use (e.g., gpu:0 for the first GPU, gpu:1,2 for the second and third GPUs). Alternatively, use CPU (--device cpu). ``` When executing the above command, the default formula recognition pipeline configuration file is loaded. If you need to customize the configuration file, you can run the following command to obtain it:paddlex --get_pipeline_config formula_recognition
After execution, the formula recognition pipeline configuration file will be saved in the current directory. If you wish to customize the save location, you can run the following command (assuming the custom save location is ./my_path):
paddlex --get_pipeline_config formula_recognition --save_path ./my_path
After obtaining the Pipeline configuration file, replace --pipeline with the configuration file's save path to make the configuration file effective. For example, if the configuration file is saved as ./formula_recognition.yaml, simply execute:
paddlex --pipeline ./formula_recognition.yaml --input general_formula_recognition.png --device gpu:0
Here, parameters such as --model and --device do not need to be specified, as they will use the parameters in the configuration file. If parameters are still specified, the specified parameters will take precedence.
{'input_path': 'general_formula_recognition.png', 'layout_result': {'input_path': 'general_formula_recognition.png', 'boxes': [{'cls_id': 3, 'label': 'number', 'score': 0.7580855488777161, 'coordinate': [1028.3635, 205.46213, 1038.953, 222.99033]}, {'cls_id': 0, 'label': 'paragraph_title', 'score': 0.8882032632827759, 'coordinate': [272.75305, 204.50894, 433.7473, 226.17996]}, {'cls_id': 2, 'label': 'text', 'score': 0.9685840606689453, 'coordinate': [272.75928, 282.17773, 1041.9316, 374.44687]}, {'cls_id': 2, 'label': 'text', 'score': 0.9559416770935059, 'coordinate': [272.39056, 385.54114, 1044.1521, 443.8598]}, {'cls_id': 2, 'label': 'text', 'score': 0.9610629081726074, 'coordinate': [272.40817, 467.2738, 1045.1033, 563.4855]}, {'cls_id': 7, 'label': 'formula', 'score': 0.8916195034980774, 'coordinate': [503.45743, 594.6236, 1040.6804, 619.73895]}, {'cls_id': 2, 'label': 'text', 'score': 0.973675549030304, 'coordinate': [272.32007, 648.8599, 1040.8702, 775.15686]}, {'cls_id': 7, 'label': 'formula', 'score': 0.9038916230201721, 'coordinate': [554.2307, 803.5825, 1040.4657, 855.3159]}, {'cls_id': 2, 'label': 'text', 'score': 0.9025381803512573, 'coordinate': [272.535, 875.1402, 573.1086, 898.3587]}, {'cls_id': 2, 'label': 'text', 'score': 0.8336610794067383, 'coordinate': [317.48013, 909.60864, 966.8498, 933.7868]}, {'cls_id': 2, 'label': 'text', 'score': 0.8779091238975525, 'coordinate': [19.704018, 653.322, 72.433235, 1215.1992]}, {'cls_id': 2, 'label': 'text', 'score': 0.8832409977912903, 'coordinate': [272.13028, 958.50806, 1039.7928, 1019.476]}, {'cls_id': 7, 'label': 'formula', 'score': 0.9088466167449951, 'coordinate': [517.1226, 1042.3978, 1040.2208, 1095.7457]}, {'cls_id': 2, 'label': 'text', 'score': 0.9587949514389038, 'coordinate': [272.03336, 1112.9269, 1041.0201, 1206.8417]}, {'cls_id': 2, 'label': 'text', 'score': 0.8885666131973267, 'coordinate': [271.7495, 1231.8752, 710.44495, 1255.7981]}, {'cls_id': 7, 'label': 'formula', 'score': 0.8907185196876526, 'coordinate': [581.2295, 1287.4525, 1039.8014, 1312.772]}, {'cls_id': 2, 'label': 'text', 'score': 0.9559596180915833, 'coordinate': [273.1827, 1341.421, 1041.0299, 1401.7255]}, {'cls_id': 2, 'label': 'text', 'score': 0.875311553478241, 'coordinate': [272.8338, 1427.3711, 789.7108, 1451.1359]}, {'cls_id': 7, 'label': 'formula', 'score': 0.9152213931083679, 'coordinate': [524.9582, 1474.8136, 1041.6333, 1530.7142]}, {'cls_id': 2, 'label': 'text', 'score': 0.9584835767745972, 'coordinate': [272.81665, 1549.524, 1042.9962, 1608.7157]}]}, 'ocr_result': {}, 'table_result': [], 'dt_polys': [array([[ 503.45743, 594.6236 ],
[1040.6804 , 594.6236 ],
[1040.6804 , 619.73895],
[ 503.45743, 619.73895]], dtype=float32), array([[ 554.2307, 803.5825],
[1040.4657, 803.5825],
[1040.4657, 855.3159],
[ 554.2307, 855.3159]], dtype=float32), array([[ 517.1226, 1042.3978],
[1040.2208, 1042.3978],
[1040.2208, 1095.7457],
[ 517.1226, 1095.7457]], dtype=float32), array([[ 581.2295, 1287.4525],
[1039.8014, 1287.4525],
[1039.8014, 1312.772 ],
[ 581.2295, 1312.772 ]], dtype=float32), array([[ 524.9582, 1474.8136],
[1041.6333, 1474.8136],
[1041.6333, 1530.7142],
[ 524.9582, 1530.7142]], dtype=float32)], 'rec_formula': ['F({\bf x})=C(F_{1}(x_{1}),\cdot\cdot\cdot,F_{N}(x_{N})).\qquad\qquad\qquad(1)', 'p(\mathbf{x})=c(\mathbf{u})\prod_{i}p(x_{i}).\qquad\qquad\qquad\qquad\qquad\quad\quad~~\quad~~~~~~~~~~~~~~~(2)', 'H_{c}({\bf x})=-\int_{{\bf{u}}}c({\bf{u}})\log c({\bf{u}})d{\bf{u}}.~~~~~~~~~~~~~~~~~~~~~(3)', 'I({\bf x})=-H_{c}({\bf x}).\qquad\qquad\qquad\qquad(4)', 'H({\bf x})=\sum_{i}H(x_{i})+H_{c}({\bf x}).\eqno\qquad\qquad\qquad(5)']}
Where dt_polys represents the coordinates of the detected formula area, and rec_formula is the detected formula.
The visualized image not saved by default. You can customize the save path through `--save_path`, and then all results will be saved in the specified path. Formula recognition visualization requires a separate environment configuration. Please refer to [2.3 Formula Recognition Pipeline Visualization](#23-formula-recognition-pipeline-visualization) to install the LaTeX rendering engine.
#### 2.2 Python Script Integration
* Quickly perform inference on the pipeline with just a few lines of code, taking the formula recognition pipeline as an example:
```python
from paddlex import create_pipeline
pipeline = create_pipeline(pipeline="formula_recognition")
output = pipeline.predict("general_formula_recognition.png")
for res in output:
res.print()
```
> ❗ The results obtained from running the Python script are the same as those from the command line.
The Python script above executes the following steps:
（1）Instantiate the formula recognition pipeline object using `create_pipeline`: Specific parameter descriptions are as follows:
| Parameter | Description | Type | Default |
|---|---|---|---|
pipeline |
The name of the pipeline or the path to the pipeline configuration file. If it is the name of the pipeline, it must be supported by PaddleX. | str |
None |
device |
The device for pipeline model inference. Supports: "gpu", "cpu". | str |
gpu |
use_hpip |
Whether to enable high-performance inference, only available if the pipeline supports it. | bool |
False |
| Parameter Type | Parameter Description |
|---|---|
| Python Var | Supports directly passing in Python variables, such as numpy.ndarray representing image data. |
| str | Supports passing in the path of the file to be predicted, such as the local path of an image file: /root/data/img.jpg. |
| str | Supports passing in the URL of the file to be predicted, such as the network URL of an image file: Example. |
| str | Supports passing in a local directory, which should contain files to be predicted, such as the local path: /root/data/. |
| dict | Supports passing in a dictionary type, where the key needs to correspond to a specific task, such as "img" for image classification tasks. The value of the dictionary supports the above types of data, for example: {"img": "/root/data1"}. |
| list | Supports passing in a list, where the list elements need to be of the above types of data, such as [numpy.ndarray, numpy.ndarray], ["/root/data/img1.jpg", "/root/data/img2.jpg"], ["/root/data1", "/root/data2"], [{"img": "/root/data1"}, {"img": "/root/data2/img.jpg"}]. |
| Method | Description | Method Parameters |
|---|---|---|
| Prints results to the terminal | - format_json: bool, whether to format the output content with json indentation, default is True;- indent: int, json formatting setting, only valid when format_json is True, default is 4;- ensure_ascii: bool, json formatting setting, only valid when format_json is True, default is False; |
|
| save_to_json | Saves results as a json file | - save_path: str, the path to save the file, when it's a directory, the saved file name is consistent with the input file type;- indent: int, json formatting setting, default is 4;- ensure_ascii: bool, json formatting setting, default is False; |
| save_to_img | Saves results as an image file | - save_path: str, the path to save the file, when it's a directory, the saved file name is consistent with the input file type; |
For main operations provided by the service:
200, and the response body properties are as follows:| Name | Type | Description |
|---|---|---|
errorCode |
integer |
Error code. Fixed as 0. |
errorMsg |
string |
Error description. Fixed as "Success". |
The response body may also have a result property of type object, which stores the operation result information.
| Name | Type | Description |
|---|---|---|
errorCode |
integer |
Error code. Same as the response status code. |
errorMsg |
string |
Error description. |
Main operations provided by the service:
inferObtain formula recognition results from an image.
POST /formula-recognition
| Name | Type | Description | Required |
|---|---|---|---|
image |
string |
The URL of an image file accessible by the service or the Base64 encoded result of the image file content. | Yes |
inferenceParams |
object |
Inference parameters. | No |
Properties of inferenceParams:
| Name | Type | Description | Required |
|---|---|---|---|
maxLongSide |
integer |
During inference, if the length of the longer side of the input image for the layout detection model is greater than maxLongSide, the image will be scaled so that the length of the longer side equals maxLongSide. |
No |
result in the response body has the following properties:| Name | Type | Description |
|---|---|---|
formulas |
array |
Positions and contents of formulas. |
image |
string |
Formula recognition result image with detected formula positions annotated. The image is in JPEG format and encoded in Base64. |
Each element in formulas is an object with the following properties:
| Name | Type | Description |
|---|---|---|
poly |
array |
Formula position. Elements in the array are the vertex coordinates of the polygon enclosing the formula. |
latex |
string |
Formula content. |
Example of result:
{
"formulas": [
{
"poly": [
[
444.0,
244.0
],
[
705.4,
244.5
],
[
705.8,
311.3
],
[
444.1,
311.0
]
],
"latex": "F({\bf x})=C(F_{1}(x_{1}),\cdot\cdot\cdot,F_{N}(x_{N})).\qquad\qquad\qquad(1)"
}
],
"image": "xxxxxx"
}
import base64
import requests
API_URL = "http://localhost:8080/formula-recognition"
image_path = "./demo.jpg"
output_image_path = "./out.jpg"
with open(image_path, "rb") as file:
image_bytes = file.read()
image_data = base64.b64encode(image_bytes).decode("ascii")
payload = {"image": image_data}
response = requests.post(API_URL, json=payload)
assert response.status_code == 200
result = response.json()["result"]
with open(output_image_path, "wb") as file:
file.write(base64.b64decode(result["image"]))
print(f"Output image saved at {output_image_path}")
print("\nDetected formulas:")
print(result["formulas"])
#include <iostream>
#include "cpp-httplib/httplib.h" // https://github.com/Huiyicc/cpp-httplib
#include "nlohmann/json.hpp" // https://github.com/nlohmann/json
#include "base64.hpp" // https://github.com/tobiaslocker/base64
int main() {
httplib::Client client("localhost:8080");
const std::string imagePath = "./demo.jpg";
const std::string outputImagePath = "./out.jpg";
httplib::Headers headers = {
{"Content-Type", "application/json"}
};
std::ifstream file(imagePath, std::ios::binary | std::ios::ate);
std::streamsize size = file.tellg();
file.seekg(0, std::ios::beg);
std::vector<char> buffer(size);
if (!file.read(buffer.data(), size)) {
std::cerr << "Error reading file." << std::endl;
return 1;
}
std::string bufferStr(reinterpret_cast<const char*>(buffer.data()), buffer.size());
std::string encodedImage = base64::to_base64(bufferStr);
nlohmann::json jsonObj;
jsonObj["image"] = encodedImage;
std::string body = jsonObj.dump();
auto response = client.Post("/formula-recognition", headers, body, "application/json");
if (response && response->status == 200) {
nlohmann::json jsonResponse = nlohmann::json::parse(response->body);
auto result = jsonResponse["result"];
encodedImage = result["image"];
std::string decodedString = base64::from_base64(encodedImage);
std::vector<unsigned char> decodedImage(decodedString.begin(), decodedString.end());
std::ofstream outputImage(outPutImagePath, std::ios::binary | std::ios::out);
if (outputImage.is_open()) {
outputImage.write(reinterpret_cast<char*>(decodedImage.data()), decodedImage.size());
outputImage.close();
std::cout << "Output image saved at " << outPutImagePath << std::endl;
} else {
std::cerr << "Unable to open file for writing: " << outPutImagePath << std::endl;
}
auto formulas = result["formulas"];
std::cout << "\nDetected formulas:" << std::endl;
for (const auto& formula : formulas) {
std::cout << formula << std::endl;
}
} else {
std::cout << "Failed to send HTTP request." << std::endl;
return 1;
}
return 0;
}
import okhttp3.*;
import com.fasterxml.jackson.databind.ObjectMapper;
import com.fasterxml.jackson.databind.JsonNode;
import com.fasterxml.jackson.databind.node.ObjectNode;
import java.io.File;
import java.io.FileOutputStream;
import java.io.IOException;
import java.util.Base64;
public class Main {
public static void main(String[] args) throws IOException {
String API_URL = "http://localhost:8080/formula-recognition";
String imagePath = "./demo.jpg";
String outputImagePath = "./out.jpg";
File file = new File(imagePath);
byte[] fileContent = java.nio.file.Files.readAllBytes(file.toPath());
String imageData = Base64.getEncoder().encodeToString(fileContent);
ObjectMapper objectMapper = new ObjectMapper();
ObjectNode params = objectMapper.createObjectNode();
params.put("image", imageData);
OkHttpClient client = new OkHttpClient();
MediaType JSON = MediaType.Companion.get("application/json; charset=utf-8");
RequestBody body = RequestBody.Companion.create(params.toString(), JSON);
Request request = new Request.Builder()
.url(API_URL)
.post(body)
.build();
try (Response response = client.newCall(request).execute()) {
if (response.isSuccessful()) {
String responseBody = response.body().string();
JsonNode resultNode = objectMapper.readTree(responseBody);
JsonNode result = resultNode.get("result");
String base64Image = result.get("image").asText();
JsonNode formulas = result.get("formulas");
byte[] imageBytes = Base64.getDecoder().decode(base64Image);
try (FileOutputStream fos = new FileOutputStream(outputImagePath)) {
fos.write(imageBytes);
}
System.out.println("Output image saved at " + outputImagePath);
System.out.println("\nDetected formulas: " + formulas.toString());
} else {
System.err.println("Request failed with code: " + response.code());
}
}
}
}
package main
import (
"bytes"
"encoding/base64"
"encoding/json"
"fmt"
"io/ioutil"
"net/http"
)
func main() {
API_URL := "http://localhost:8080/formula-recognition"
imagePath := "./demo.jpg"
outputImagePath := "./out.jpg"
imageBytes, err := ioutil.ReadFile(imagePath)
if err != nil {
fmt.Println("Error reading image file:", err)
return
}
imageData := base64.StdEncoding.EncodeToString(imageBytes)
payload := map[string]string{"image": imageData}
payloadBytes, err := json.Marshal(payload)
if err != nil {
fmt.Println("Error marshaling payload:", err)
return
}
client := &http.Client{}
req, err := http.NewRequest("POST", API_URL, bytes.NewBuffer(payloadBytes))
if err != nil {
fmt.Println("Error creating request:", err)
return
}
res, err := client.Do(req)
if err != nil {
fmt.Println("Error sending request:", err)
return
}
defer res.Body.Close()
body, err := ioutil.ReadAll(res.Body)
if err != nil {
fmt.Println("Error reading response body:", err)
return
}
type Response struct {
Result struct {
Image string `json:"image"`
Formulas []map[string]interface{} `json:"formulas"`
} `json:"result"`
}
var respData Response
err = json.Unmarshal([]byte(string(body)), &respData)
if err != nil {
fmt.Println("Error unmarshaling response body:", err)
return
}
outputImageData, err := base64.StdEncoding.DecodeString(respData.Result.Image)
if err != nil {
fmt.Println("Error decoding base64 image data:", err)
return
}
err = ioutil.WriteFile(outputImagePath, outputImageData, 0644)
if err != nil {
fmt.Println("Error writing image to file:", err)
return
}
fmt.Printf("Image saved at %s.jpg\n", outputImagePath)
fmt.Println("\nDetected formulas:")
for _, formula := range respData.Result.Formulas {
fmt.Println(formula)
}
}
using System;
using System.IO;
using System.Net.Http;
using System.Net.Http.Headers;
using System.Text;
using System.Threading.Tasks;
using Newtonsoft.Json.Linq;
class Program
{
static readonly string API_URL = "http://localhost:8080/formula-recognition";
static readonly string imagePath = "./demo.jpg";
static readonly string outputImagePath = "./out.jpg";
static async Task Main(string[] args)
{
var httpClient = new HttpClient();
byte[] imageBytes = File.ReadAllBytes(imagePath);
string image_data = Convert.ToBase64String(imageBytes);
var payload = new JObject{ { "image", image_data } };
var content = new StringContent(payload.ToString(), Encoding.UTF8, "application/json");
HttpResponseMessage response = await httpClient.PostAsync(API_URL, content);
response.EnsureSuccessStatusCode();
string responseBody = await response.Content.ReadAsStringAsync();
JObject jsonResponse = JObject.Parse(responseBody);
string base64Image = jsonResponse["result"]["image"].ToString();
byte[] outputImageBytes = Convert.FromBase64String(base64Image);
File.WriteAllBytes(outputImagePath, outputImageBytes);
Console.WriteLine($"Output image saved at {outputImagePath}");
Console.WriteLine("\nDetected formulas:");
Console.WriteLine(jsonResponse["result"]["formulas"].ToString());
}
}
const axios = require('axios');
const fs = require('fs');
const API_URL = 'http://localhost:8080/formula-recognition'
const imagePath = './demo.jpg'
const outputImagePath = "./out.jpg";
let config = {
method: 'POST',
maxBodyLength: Infinity,
url: API_URL,
data: JSON.stringify({
'image': encodeImageToBase64(imagePath)
})
};
function encodeImageToBase64(filePath) {
const bitmap = fs.readFileSync(filePath);
return Buffer.from(bitmap).toString('base64');
}
axios.request(config)
.then((response) => {
const result = response.data["result"];
const imageBuffer = Buffer.from(result["image"], 'base64');
fs.writeFile(outputImagePath, imageBuffer, (err) => {
if (err) throw err;
console.log(`Output image saved at ${outputImagePath}`);
});
console.log("\nDetected formulas:");
console.log(result["formulas"]);
})
.catch((error) => {
console.log(error);
});
<?php
$API_URL = "http://localhost:8080/formula-recognition";
$image_path = "./demo.jpg";
$output_image_path = "./out.jpg";
$image_data = base64_encode(file_get_contents($image_path));
$payload = array("image" => $image_data);
$ch = curl_init($API_URL);
curl_setopt($ch, CURLOPT_POST, true);
curl_setopt($ch, CURLOPT_POSTFIELDS, json_encode($payload));
curl_setopt($ch, CURLOPT_HTTPHEADER, array('Content-Type: application/json'));
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
$response = curl_exec($ch);
curl_close($ch);
$result = json_decode($response, true)["result"];
file_put_contents($output_image_path, base64_decode($result["image"]));
echo "Output image saved at " . $output_image_path . "\n";
echo "\nDetected formulas:\n";
print_r($result["formulas"]);
?>