How to collision detection?

Processing Libraries
1

Hello

I try to make a Mario Bros Game. I need some help with the collision. It already detects collision by checking if the tiles around him are an object tile (tile with other value than -1). The problem is that there is still a gap between the character and the wall. I know why but I can not think of a way of solving this.

import ptmx.*;

Ptmx map;
PImage image;
boolean left, right, jump, crouch;
PVector position, velocity, origin;

void setup(){
  size(1200,480);
  map = new Ptmx(this, "map.tmx");
  image = loadImage("MarioStanding.png");
  position = new PVector(0,0);
  velocity= new PVector(4,4);
}
void draw(){ 
    if(jump == true && !collision_detected(position, "up")){
      position.y-=velocity.y;
    }
    if(left == true && !collision_detected(position, "left")){
      position.x-=velocity.x;
    }
    if(crouch == true && !collision_detected(position, "down")){
      position.y+=velocity.y;
    }
    if(right == true && !collision_detected(position, "right")){
      position.x+=velocity.x;
    }
    
  background(map.getBackgroundColor());
  map.draw(0,0);
  image(image,position.x,position.y);
}
boolean collision_detected(PVector pPosition, String pDirection){
  int x = 0;
  int y = 0;
  /*
      case for when character is at pixel 16 because pixel 16 should be still in tile 0 but is in tile x + 1 because 16 / tile_size (16) is 1 ( tile = 1 )
  */
  if((pPosition.x + image.width) % 16 == 0){
    x = 1;
  }
  if((pPosition.y + image.height) % 16 == 0){
    y = 1;
  }
  int character_left = (int)(pPosition.x / 16);
  int character_right = (int)((pPosition.x + image.width) / 16 - x);
  int character_top = (int)(pPosition.y / 16);
  int character_bottom = (int)((pPosition.y + image.height) / 16 - y);
  boolean any_collision = false;
  
  int a = 0, b = 0;
  if(pDirection.equals("left") || pDirection.equals("right")){
    a = 0;
    b = 1;
  } else if(pDirection.equals("up") || pDirection.equals("down")) {
    a = 1;
    b = 0;
  }
  
  int i = character_left - b;
  int k = character_right + b;
  if(pDirection.equals("right")){
    i = character_right + b; // set i to character_right because only right columns need to be checked for collision
  } else if(pDirection.equals("left")){
    k = character_left - b;
  }
  for(; i <= k; i++){
    int j = character_top - a;
    int l = character_bottom + a;
    if(pDirection.equals("down")){
      j = character_bottom + a; // set j to character_bottom because only bottom rows need to be checked for collision
    } else if(pDirection.equals("up")){
      l = character_top - a;
    }
    for(; j <= l; j++){
      int tile_id = map.getTileIndex(0, i, j);
      switch(tile_id){
        case 0: case 1: case 2: case 3: case 4: case 5: case 6:
          any_collision = true;
          break;
        default:
          break;
      } 
    }
  }
  
  return any_collision;
}
void keyReleased(){
  if(key == 'w'){
    jump = false;
  }
  if(key == 'a'){
    left = false;
  }
  if(key == 's'){
    crouch = false;
  }
  if(key == 'd'){
    right = false;
  }
}
void keyPressed(){
  if(key == 'w'){
    jump = true;
  }
  if(key == 'a'){
    left = true;
  }
  if(key == 's'){
    crouch = true;
  }
  if(key == 'd'){
    right = true;
  }
}