Implement ctc prefix beam search decode for TextRecognitionModel.

The algorithm is based on Hannun's paper: First-Pass Large Vocabulary
Continuous Speech Recognition using Bi-Directional Recurrent DNNs

doc/tutorials/dnn/dnn_text_spotting/dnn_text_spotting.markdown

@@ -26,6 +26,11 @@ Before recognition, you should `setVocabulary` and `setDecodeType`.
     - `T` is the sequence length
     - `B` is the batch size (only support `B=1` in inference)
     - and `Dim` is the length of vocabulary +1('Blank' of CTC is at the index=0 of Dim).
+- "CTC-prefix-beam-search", the output of the text recognition model should be a probability matrix same with "CTC-greedy".
+    - The algorithm is proposed at Hannun's [paper](https://arxiv.org/abs/1408.2873).
+    - `setDecodeOptsCTCPrefixBeamSearch` could be used to control the beam size in search step.
+    - To futher optimize for big vocabulary, a new option `vocPruneSize` is introduced to avoid iterate the whole vocbulary
+       but only the number of `vocPruneSize` tokens with top probabilty.
 
 @ref cv::dnn::TextRecognitionModel::recognize() is the main function for text recognition.
 - The input image should be a cropped text image or an image with `roiRects`

modules/dnn/include/opencv2/dnn/dnn.hpp

@@ -1373,7 +1373,9 @@ class CV_EXPORTS_W_SIMPLE TextRecognitionModel : public Model
 
     /**
      * @brief Set the decoding method of translating the network output into string
-     * @param[in] decodeType The decoding method of translating the network output into string: {'CTC-greedy': greedy decoding for the output of CTC-based methods}
+     * @param[in] decodeType The decoding method of translating the network output into string, currently supported type:
+     *    - `"CTC-greedy"` greedy decoding for the output of CTC-based methods
+     *    - `"CTC-prefix-beam-search"` Prefix beam search decoding for the output of CTC-based methods
      */
     CV_WRAP
     TextRecognitionModel& setDecodeType(const std::string& decodeType);
@@ -1385,6 +1387,15 @@ class CV_EXPORTS_W_SIMPLE TextRecognitionModel : public Model
     CV_WRAP
     const std::string& getDecodeType() const;
 
+    /**
+     * @brief Set the decoding method options for `"CTC-prefix-beam-search"` decode usage
+     * @param[in] beamSize Beam size for search
+     * @param[in] vocPruneSize Parameter to optimize big vocabulary search,
+     * only take top @p vocPruneSize tokens in each search step, @p vocPruneSize <= 0 stands for disable this prune.
+     */
+    CV_WRAP
+    TextRecognitionModel& setDecodeOptsCTCPrefixBeamSearch(int beamSize, int vocPruneSize = 0);
+
     /**
      * @brief Set the vocabulary for recognition.
      * @param[in] vocabulary the associated vocabulary of the network.

modules/dnn/src/math_utils.hpp

@@ -0,0 +1,83 @@
+// This file is part of OpenCV project.
+// It is subject to the license terms in the LICENSE file found in the top-level directory
+// of this distribution and at http://opencv.org/license.html.
+
+// Code is borrowed from https://github.com/kaldi-asr/kaldi/blob/master/src/base/kaldi-math.h
+
+// base/kaldi-math.h
+
+// Copyright 2009-2011  Ondrej Glembek;  Microsoft Corporation;  Yanmin Qian;
+//                      Jan Silovsky;  Saarland University
+//
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef __OPENCV_DNN_MATH_UTILS_HPP__
+#define __OPENCV_DNN_MATH_UTILS_HPP__
+
+#ifdef OS_QNX
+#include <math.h>
+#else
+#include <cmath>
+#endif
+
+#include <limits>
+
+#ifndef FLT_EPSILON
+#define FLT_EPSILON 1.19209290e-7f
+#endif
+
+namespace cv { namespace dnn {
+
+const float kNegativeInfinity = -std::numeric_limits<float>::infinity();
+
+const float kMinLogDiffFloat = std::log(FLT_EPSILON);
+
+#if !defined(_MSC_VER) || (_MSC_VER >= 1700)
+inline float Log1p(float x) {  return log1pf(x); }
+#else
+inline float Log1p(float x) {
+  const float cutoff = 1.0e-07;
+  if (x < cutoff)
+    return x - 2 * x * x;
+  else
+    return Log(1.0 + x);
+}
+#endif
+
+inline float Exp(float x) { return expf(x); }
+
+inline float LogAdd(float x, float y) {
+  float diff;
+  if (x < y) {
+    diff = x - y;
+    x = y;
+  } else {
+    diff = y - x;
+  }
+  // diff is negative.  x is now the larger one.
+
+  if (diff >= kMinLogDiffFloat) {
+    float res;
+    res = x + Log1p(Exp(diff));
+    return res;
+  } else {
+    return x;  // return the larger one.
+  }
+}
+
+}}  // namespace
+
+#endif  // __OPENCV_DNN_MATH_UTILS_HPP__