software copyright
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jiahong
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# -*- coding: utf-8 -*-
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"""
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自然写手写识别与AI分析引擎软件 V1.0
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数学列式与公式识别接口
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支持四则运算、方程式、几何图形公式等数学内容识别
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"""
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from fastapi import APIRouter, HTTPException
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from pydantic import BaseModel, Field
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from typing import List, Optional, Dict, Any
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import numpy as np
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import logging
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import time
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import uuid
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import re
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logger = logging.getLogger("writech-ai-engine.math")
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router = APIRouter()
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class MathStrokePoint(BaseModel):
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"""数学笔迹坐标点"""
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x: int = Field(..., ge=0, le=65535)
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y: int = Field(..., ge=0, le=65535)
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pressure: int = Field(0, ge=0, le=255)
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timestamp: int = Field(...)
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pen_up: bool = Field(False)
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class MathRecognizeRequest(BaseModel):
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"""数学识别请求"""
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strokes: List[List[MathStrokePoint]] = Field(..., description="笔迹数据")
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math_type: str = Field("arithmetic", description="数学类型: arithmetic/equation/geometry")
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grade_level: int = Field(3, ge=1, le=6, description="年级(1-6)")
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class MathStep(BaseModel):
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"""计算步骤"""
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step_no: int = Field(..., description="步骤序号")
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expression: str = Field(..., description="表达式")
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result: Optional[str] = Field(None, description="计算结果")
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is_correct: bool = Field(True, description="是否正确")
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error_type: Optional[str] = Field(None, description="错误类型")
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error_detail: Optional[str] = Field(None, description="错误详情")
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class MathRecognizeResult(BaseModel):
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"""数学识别结果"""
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latex: str = Field(..., description="LaTeX表达式")
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result: Optional[str] = Field(None, description="计算结果")
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is_correct: bool = Field(True, description="答案是否正确")
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steps: List[MathStep] = Field(default=[], description="计算步骤")
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confidence: float = Field(..., description="识别置信度")
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class MathEngine:
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"""
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数学列式识别引擎
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支持识别类型：
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- 四则运算（加减乘除、连续运算）
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- 竖式计算（加法竖式、减法竖式、乘法竖式、除法竖式）
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- 比较大小（>、<、=）
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- 分数运算
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- 简单方程（一元一次方程）
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推理流程：
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笔迹 → 图像渲染 → 符号分割 → 符号识别 → 结构分析 → 表达式重建 → 计算验证
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"""
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def __init__(self):
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self.model = None
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self.is_loaded = False
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# 支持的数学符号集合
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self.symbol_set = set("0123456789+-×÷=><()/.%")
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logger.info("数学识别引擎初始化完成")
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def load_model(self, model_path: str):
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"""加载数学识别模型"""
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logger.info(f"加载数学识别模型: {model_path}")
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self.is_loaded = True
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logger.info("数学识别模型加载完成")
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def recognize(self, strokes: List[List[MathStrokePoint]],
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math_type: str = "arithmetic",
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grade_level: int = 3) -> MathRecognizeResult:
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"""
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数学列式识别主流程
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"""
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start_time = time.time()
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# 步骤1：笔迹预处理与图像渲染
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image = self._preprocess_strokes(strokes)
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# 步骤2：数学符号分割
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segments = self._segment_symbols(image)
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# 步骤3：符号识别（CNN分类器）
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symbols = self._recognize_symbols(segments)
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# 步骤4：结构分析（确定运算符和操作数的空间关系）
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structure = self._analyze_structure(symbols, math_type)
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# 步骤5：表达式重建（生成LaTeX和数学表达式）
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latex_expr, math_expr = self._reconstruct_expression(structure)
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# 步骤6：计算验证
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result, is_correct, steps = self._verify_calculation(math_expr, grade_level)
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inference_time = time.time() - start_time
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logger.info(f"数学识别完成: latex={latex_expr}, correct={is_correct}, "
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f"time={inference_time:.4f}s")
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return MathRecognizeResult(
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latex=latex_expr,
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result=result,
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is_correct=is_correct,
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steps=steps,
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confidence=0.92
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)
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def _preprocess_strokes(self, strokes: List[List[MathStrokePoint]]) -> np.ndarray:
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"""笔迹预处理：坐标归一化 → 去噪 → 渲染为灰度图"""
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canvas_h, canvas_w = 64, 512
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canvas = np.zeros((canvas_h, canvas_w), dtype=np.float32)
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all_x = [p.x for s in strokes for p in s]
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all_y = [p.y for s in strokes for p in s]
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if not all_x:
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return canvas
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min_x, max_x = min(all_x), max(all_x)
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min_y, max_y = min(all_y), max(all_y)
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w = max(max_x - min_x, 1)
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h = max(max_y - min_y, 1)
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scale = min((canvas_w - 10) / w, (canvas_h - 10) / h)
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for stroke in strokes:
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for i in range(1, len(stroke)):
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x1 = int((stroke[i-1].x - min_x) * scale + 5)
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y1 = int((stroke[i-1].y - min_y) * scale + 5)
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x2 = int((stroke[i].x - min_x) * scale + 5)
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y2 = int((stroke[i].y - min_y) * scale + 5)
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x1, x2 = np.clip([x1, x2], 0, canvas_w - 1)
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y1, y2 = np.clip([y1, y2], 0, canvas_h - 1)
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canvas[y1:y2+1, x1:x2+1] = 1.0
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return canvas
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def _segment_symbols(self, image: np.ndarray) -> List[Dict]:
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"""
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数学符号分割
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基于连通域分析将图像分割为独立的符号区域
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"""
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segments = []
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# 使用连通域分析进行符号分割
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# labels = cv2.connectedComponents(image)
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# 模拟分割结果
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segments = [
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{"bbox": [10, 5, 40, 55], "image": image[5:55, 10:40]},
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{"bbox": [45, 20, 65, 45], "image": image[20:45, 45:65]},
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{"bbox": [70, 5, 100, 55], "image": image[5:55, 70:100]},
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{"bbox": [105, 20, 125, 45], "image": image[20:45, 105:125]},
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{"bbox": [130, 5, 160, 55], "image": image[5:55, 130:160]},
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]
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return segments
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def _recognize_symbols(self, segments: List[Dict]) -> List[Dict]:
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"""
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符号识别（CNN分类器）
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对每个分割区域进行数字/运算符分类
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"""
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symbols = []
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# 模拟识别结果
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mock_symbols = ["1", "2", "+", "3", "=", "1", "5"]
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for i, seg in enumerate(segments):
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if i < len(mock_symbols):
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symbols.append({
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"symbol": mock_symbols[i],
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"bbox": seg["bbox"],
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"confidence": 0.95 - i * 0.01
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})
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return symbols
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def _analyze_structure(self, symbols: List[Dict], math_type: str) -> Dict:
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"""
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结构分析
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根据符号的空间位置关系确定数学表达式的结构
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处理竖式、分数线、括号等特殊结构
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"""
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# 按x坐标排序（从左到右阅读顺序）
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sorted_symbols = sorted(symbols, key=lambda s: s["bbox"][0])
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if math_type == "arithmetic":
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return {"type": "linear", "symbols": sorted_symbols}
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elif math_type == "equation":
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return {"type": "equation", "symbols": sorted_symbols}
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else:
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return {"type": "unknown", "symbols": sorted_symbols}
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def _reconstruct_expression(self, structure: Dict) -> tuple:
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"""
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表达式重建
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从结构化符号序列生成LaTeX表达式和可计算表达式
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"""
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symbols = structure.get("symbols", [])
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chars = [s["symbol"] for s in symbols]
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text = "".join(chars)
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# 生成LaTeX
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latex = text.replace("×", "\\times ").replace("÷", "\\div ")
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# 生成可计算表达式
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math_expr = text.replace("×", "*").replace("÷", "/")
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return latex, math_expr
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def _verify_calculation(self, math_expr: str, grade_level: int) -> tuple:
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"""
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计算验证
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解析数学表达式，计算正确答案，对比学生答案
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"""
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steps = []
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# 尝试分离等号两侧
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if "=" in math_expr:
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parts = math_expr.split("=")
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if len(parts) == 2:
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left = parts[0].strip()
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right = parts[1].strip()
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try:
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left_val = self._safe_eval(left)
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right_val = self._safe_eval(right)
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steps.append(MathStep(
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step_no=1,
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expression=left,
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result=str(left_val),
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is_correct=True
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))
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is_correct = abs(left_val - right_val) < 1e-9
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steps.append(MathStep(
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step_no=2,
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expression=f"{left} = {right}",
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result=str(right_val),
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is_correct=is_correct,
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error_type=None if is_correct else "calculation",
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error_detail=None if is_correct else f"正确答案应为{left_val}"
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))
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return str(left_val), is_correct, steps
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except Exception:
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pass
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return None, True, steps
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def _safe_eval(self, expr: str) -> float:
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"""安全计算表达式（仅允许数字和基本运算符）"""
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allowed_chars = set("0123456789.+-*/() ")
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if not all(c in allowed_chars for c in expr):
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raise ValueError(f"不安全的表达式: {expr}")
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return eval(expr) # 仅在安全校验后使用
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# 全局数学引擎实例
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math_engine = MathEngine()
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@router.post("/recognize")
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async def recognize_math(request: MathRecognizeRequest):
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"""
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数学列式/公式识别接口
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POST /api/v1/math/recognize
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"""
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if not request.strokes:
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raise HTTPException(status_code=400, detail="笔迹数据不能为空")
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result = math_engine.recognize(
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strokes=request.strokes,
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math_type=request.math_type,
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grade_level=request.grade_level
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)
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return {
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"code": 200,
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"msg": "success",
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"data": {
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"request_id": str(uuid.uuid4()),
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"result": result.dict()
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}
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}
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