diff --git a/internal/captcha/handler.go b/internal/captcha/handler.go
index 7f49d7d..713ef04 100644
--- a/internal/captcha/handler.go
+++ b/internal/captcha/handler.go
@@ -6,6 +6,7 @@ import (
 	"encoding/json"
 	"fmt"
 	"image"
+	"image/color"
 	"math"
 	"net/http"
 	"os"
@@ -323,14 +324,42 @@ func (h *Handler) Math(imageBase64 string) (string, error) {
 }
 
 func preprocessMath(img image.Image) ([]float32, error) {
-	resized := imaging.Resize(img, 200, 70, imaging.Lanczos)
-	rgb := imaging.Clone(resized)
+	// resize_with_padding: 保持比例缩放，白色填充
+	targetW, targetH := 200, 70
+	
+	// 计算缩放比例
+	bounds := img.Bounds()
+	srcW, srcH := bounds.Dx(), bounds.Dy()
+	ratio := min(float64(targetW)/float64(srcW), float64(targetH)/float64(srcH))
+	
+	newW := int(float64(srcW) * ratio)
+	newH := int(float64(srcH) * ratio)
+	
+	// 缩放图片
+	resized := imaging.Resize(img, newW, newH, imaging.Lanczos)
+	
+	// 创建白色背景
+	canvas := image.NewRGBA(image.Rect(0, 0, targetW, targetH))
+	white := color.RGBA{255, 255, 255, 255}
+	for x := 0; x < targetW; x++ {
+		for y := 0; y < targetH; y++ {
+			canvas.Set(x, y, white)
+		}
+	}
+	
+	// 粘贴缩放后的图片
+	for x := 0; x < newW; x++ {
+		for y := 0; y < newH; y++ {
+			canvas.Set(x, y, resized.At(x, y))
+		}
+	}
 
 	pixels := make([]float32, 3*70*200)
 	for y := 0; y < 70; y++ {
 		for x := 0; x < 200; x++ {
-			c := rgb.At(x, y)
+			c := canvas.At(x, y)
 			r, g, b, _ := c.RGBA()
+			// 归一化到 [0, 1]，然后标准化到 [-1, 1]
 			pixels[0*70*200+y*200+x] = (float32(r)/65535.0 - 0.5) / 0.5
 			pixels[1*70*200+y*200+x] = (float32(g)/65535.0 - 0.5) / 0.5
 			pixels[2*70*200+y*200+x] = (float32(b)/65535.0 - 0.5) / 0.5
@@ -341,50 +370,75 @@ func preprocessMath(img image.Image) ([]float32, error) {
 }
 
 func decodeMath(output []float32, outputShape []int64) string {
-	// 输出格式: [num_chars, batch, timesteps] = [51, 1, 19]
-	// 需要转置为 [batch, timesteps, num_chars] = [1, 19, 51]
+	// 原版逻辑：
+	// if preds.shape[1] == 1: # Batch size is 1 at dim 1 implies [T, B, C]
+	//     preds = np.transpose(preds, (1, 0, 2)) # [B, T, C]
+	// preds_idx = np.argmax(preds, axis=2) # [B, T]
+	
 	if len(outputShape) < 3 || len(output) == 0 {
 		return ""
 	}
 
-	numChars := int(outputShape[0])  // 51
-	batch := int(outputShape[1])     // 1
-	timesteps := int(outputShape[2]) // 19
-
-	// 处理动态维度（可能返回 -1）
-	if numChars <= 0 {
-		numChars = 51 // 默认字符数
-	}
-	if batch <= 0 {
-		batch = 1
-	}
-	if timesteps <= 0 {
-		// 从输出大小推断
-		timesteps = len(output) / (numChars * batch)
-	}
-
-	// 边界检查
-	if numChars <= 0 || batch <= 0 || timesteps <= 0 {
-		return ""
-	}
-
-	// 转置: output[c*batch*t + b*t + t] -> transposed[b*timesteps*numChars + t*numChars + c]
-	transposed := make([]float32, batch*timesteps*numChars)
-	for b := 0; b < batch; b++ {
+	// 输出可能是 [T, B, C] 或 [C, B, T]
+	// 判断依据：如果 shape[1] == 1，说明 batch 在中间，格式是 [T, B, C]
+	// 否则格式是 [C, B, T] 或 [num_chars, batch, timesteps]
+	
+	dim0 := int(outputShape[0])
+	dim1 := int(outputShape[1])
+	dim2 := int(outputShape[2])
+	
+	// 处理动态维度
+	if dim0 <= 0 { dim0 = 51 }
+	if dim1 <= 0 { dim1 = 1 }
+	if dim2 <= 0 { dim2 = len(output) / (dim0 * dim1) }
+	
+	var timesteps, batch, numChars int
+	var data []float32
+	
+	// 判断输出格式
+	if dim1 == 1 {
+		// 格式: [T, B, C] = [19, 1, 51]
+		// 需要转置为 [B, T, C] = [1, 19, 51]
+		timesteps = dim0
+		batch = dim1
+		numChars = dim2
+		
+		data = make([]float32, batch*timesteps*numChars)
 		for t := 0; t < timesteps; t++ {
-			for c := 0; c < numChars; c++ {
-				srcIdx := c*batch*timesteps + b*timesteps + t
-				dstIdx := b*timesteps*numChars + t*numChars + c
-				if srcIdx < len(output) && dstIdx < len(transposed) {
-					transposed[dstIdx] = output[srcIdx]
+			for b := 0; b < batch; b++ {
+				for c := 0; c < numChars; c++ {
+					srcIdx := t*batch*numChars + b*numChars + c
+					dstIdx := b*timesteps*numChars + t*numChars + c
+					if srcIdx < len(output) && dstIdx < len(data) {
+						data[dstIdx] = output[srcIdx]
+					}
+				}
+			}
+		}
+	} else {
+		// 格式: [C, B, T] = [51, 1, 19]
+		// 需要转置为 [B, T, C] = [1, 19, 51]
+		numChars = dim0
+		batch = dim1
+		timesteps = dim2
+		
+		data = make([]float32, batch*timesteps*numChars)
+		for c := 0; c < numChars; c++ {
+			for b := 0; b < batch; b++ {
+				for t := 0; t < timesteps; t++ {
+					srcIdx := c*batch*timesteps + b*timesteps + t
+					dstIdx := b*timesteps*numChars + t*numChars + c
+					if srcIdx < len(output) && dstIdx < len(data) {
+						data[dstIdx] = output[srcIdx]
+					}
 				}
 			}
 		}
 	}
-
+	
 	// CTC 解码: 对每个 timestep 取 argmax
 	result := ""
-	lastIdx := 0
+	lastIdx := -1
 
 	for t := 0; t < timesteps; t++ {
 		maxIdx := 0
@@ -392,8 +446,8 @@ func decodeMath(output []float32, outputShape []int64) string {
 
 		for c := 0; c < numChars; c++ {
 			idx := t*numChars + c
-			if idx < len(transposed) && transposed[idx] > maxProb {
-				maxProb = transposed[idx]
+			if idx < len(data) && data[idx] > maxProb {
+				maxProb = data[idx]
 				maxIdx = c
 			}
 		}
@@ -410,6 +464,13 @@ func decodeMath(output []float32, outputShape []int64) string {
 	return result
 }
 
+func min(a, b float64) float64 {
+	if a < b {
+		return a
+	}
+	return b
+}
+
 func evalMathExpression(expr string) (interface{}, error) {
 	expr = strings.ReplaceAll(expr, "×", "*")
 	expr = strings.ReplaceAll(expr, "÷", "/")